Based on the hindcast data from third-generation wave model WAVEWATCH III, this study presents a notable interannual variability of significant wave height in the northern South China Sea. As indicated by the empirical orthogonal function analysis result of the significant wave height during 1976–2005, the first mode of this analysis captures a monopole structure with maximum amplitude in the southwestern Luzon Strait. Power spectrum analysis of the first empirical orthogonal function time series indicates that the significant wave height peaks at 2.67 and 8 year periods in the northern South China Sea. The first-time series had good correlation with El Niño events, with a correlation coefficient of -0.58. By comparing frequency and total duration of the intense tropical cyclones with the significant wave height in the northern South China Sea, it is revealed that the two were associated during 1978–1998 and that the recent increase of the significant wave height is due to the increase in total duration of intense tropical cyclones during 1999–2005. The sea level pressures also support the interannual variability of significant wave height in the northern South China Sea.

Introduction

Long-term change in the wave climate is very important for the operation of offshore industries, the selection of ships routing and the risk evaluation of the future weakness to possible coastal disasters. In recent decades, considerable efforts have been devoted to study the seasonal and interannual variability of the significant wave height (SWH), extreme wave heights using the buoy observations, altimeter measurements and hindcast data (Bacon et al.,1991; Cater and Draper, 1988; Wang and Swail, 2000; Graham et al., 2001, 2002; Sasaki et al., 2005, 2006, 2007; Kako and Kubota, 2006; Weisse et al., 2007; Yong et al., 2008; Qi et al., 2010; Izaguirre et al., 2012; Osinowo et al., 2016). In particular, many works have been focused on the wave climate in the Atlantic and Pacific. Cater and Draper (1988) and Bacon and Carter (1991) used the longest-running wave record in the world to show the 0.034 m yr−1 upward trend of SWH at the seven Stones Light Vessels off the Southwest coast of England since 1962. A strong relationship between the wintertime wave climate in the North Atlantic and the North Atlantic Oscillation (NAO) was identified (WASA Group, 1998; Wang and Swail, 2000; Woolf et al., 2002). According to the wave reanalysis obtained from WW3 (Tolman, 2002), Graham and Diaz (2001) and Graham et al. (2002), it was revealed that the interannual variability of the SWH in the North Pacific, clarified the long-term upward trend of SWH in the northern storm track as evidence of an increase in winter storm activity. Based on the SWH derived from the ECMWF, Sasaki et al. (2005) demonstrated that the recent increase in extreme wave heights in the western North Pacific was due to the recent increase in total duration of intense tropical cyclones. In addition, Sasaki et al. (2006, 2007) presented the interannual variability of the summer and autumn extreme wave heights in the western North Pacific. Kako and Kubota (2006) examined the relationship between interannual variability of wintertime SWH in the North Pacific and El Niño events by applying the EOF analysis to optimally interpolated monthly mean TOPEX/Poseidon (T/P) SWH data over 1993–2000. Izaguirre et al. (2012) presented the anomalies of the 50-year return level estimates of SWH, due to interannual variability have been projected into the weather types of SOM.

The SCS (Figure 1) is the largest semi-enclosed marginal sea, located in the tropical and subtropical area which belongs to the Asian monsoon region. The SCS is also an important channel between the western Pacific and Indian Ocean. In the SCS, southwest monsoons prevail mostly in the summertime and northeast monsoons in the wintertime (Chu et al., 1997). The basic structure of upper-ocean heat and power exchange are dominated by the monsoons. The wave characteristics affected by monsoons show significant seasonal changes in the SCS (Qi and Shi, 1999). Many studies have been focused on the seasonal variability of SWH, wave characteristics under extreme weather conditions and statistical analysis of the extreme wave heights based on altimeter data (Qi and Shi, 1999) or wave hindcast data (Chu and Cheng, 2008; Qi et al., 2010; Jiang et al., 2010; Osinowo et al., 2016) in the SCS. Although the seasonal variability of SWH and the analysis of the extreme wave height have been extensively analyzed, the interannual variability of the SWH in the SCS has less been investigated. Based on the 30-year wave hindcast data during 1976–2005, this study analyzes the interannual variability of the SWH in the northern SCS and discussed its correlation with the El Niño events, as well as the tropical cyclone activity.

Data description and model validation

The wave model

The WW3 implemented in this study is a full third-generation ocean wave model developed by the National Oceanic and Atmospheric Administration/National Center for Environmental Prediction/National Weather Service (NOAA/NCEP/NWS). It's based on the WAVEWATCH I developed at Delft University of Technology (Tolman, 1989, 1991) and the WAVEWATCH II (Tolman, 1992) developed at NASA Goddard Space Flight Center. The WW3 model solves the spectral action density balance equations for directional wavenumber spectra with the full nonlinear physics, and it accounts for wind input, wave-wave interaction and dissipation due to white capping and wave-bottom interaction.

Wind fields

In this study, we use two different wind products to drive the WW3 model. One of the wind field products is from the NCEP/NCAR reanalysis atmospheric model. The spatial resolution of the data is 1.875º in longitude and 1.905º in latitude with a temporal resolution of 6 hourly. The main advantages of the NCEP/NCAR reanalysis are their physical consistency and relatively long temporal coverage (since 1 Janaury 1948 to the present). Full details of the NCEP/NCAR project and the dataset were given in Kalnay et al. (1996). Another wind field is reconstructed by using a typhoon empirical model (Holland, 1980) which would be introduced in the next section. Cubic spline interpolation is used to generate appropriate wind fields to match the spatial and temporal resolution of the WW3 model.

Typhoon wind fields

The typhoon wind field usually varies intensely. The large gradient of speed and the rapid change of wind direction in a typhoon vortex generate very complex ocean wave fields. As the NCEP/NCAR reanalysis wind speeds are lower than observation during typhoon periods (Josey et al., 2002), an experiential typhoon model (Holland, 1980) is considered in this article.
formula
(1)

is the gradient wind speed at distance R from the typhoon eye, and represent the asymptotic environmental and central pressure, respectively, is the radius of maximum winds, is the air density, f is Coriolis parameter and b is the parameter that changes the shape of the radial profile.

Adjustments are made near the periphery of the typhoon to smooth the transition velocity between the background wind fields and tropical cyclones. It is done by a weighted averaged inside and outside of the tropical cyclone (Carr and Elsberry, 1997).
formula
(2)
where Vbg is the background wind field, we use the NCEP/NCAR reanalysis data as the background wind field in this article. Vt is the translation velocity of the tropical cyclone derived from the Tropical Cyclone Best-Track Data which was issued by the Regional Specialized Meteorological Center (RSMC) Tokyo Typhoon Center, and the weight ɛ is computed by
formula
(3)
where , is the radius of zero tangential velocities inside a tropical cyclone. These adjustments provide for a smoother transition between the wind field of the tropical cyclone and the background wind field. As the radial distance to the tropical cyclone center decreasing, the weighting on the wind speed of the tropical cyclone is increasing gradually and the weighting on the background winds is decreasing.

Observation data

The buoy located in 113.59°E, 21.29°N, with the water depth is about 52 m, and is used to validate the outputs from the model forced by NCEP/NCAR wind fields and reconstructed wind fields (Figure 1). It provides 10-min averaged wind speed at 10 m and SWH, with a temporal resolution of 6 hourly. The time span of buoy is from 1 July 2001 to 1 September 2001. The number of tropical cyclones over the SCS during this period is six, including three intense tropical cyclones passing through the nearby area of the buoy. These intense tropical cyclones occurred at the end of June, early July and end of the July are shown in Figure 2, which are highlighted by the ovals.

Model set up

The domain of the model is shown in Figure 1, extending from 99°E to 130°E and 0°N to 31°N. The minimum water depth in the model is 5m and the time step is 15-min. The model is spin-up for 15 days, from 00 UTC on the 17 December 1975. The wavenumber grid is divided by 25 from 0.041 to 0.412 Hz and the wave direction spacing is 15 degrees. In order to analyze the interannual variability of the SWH in the SCS, the 6-hourly hindcasted wave parameters with spatial resolution 0.25º × 0.25º during 1976–2005 is produced by the WW3 model that used the realistic bathymetry data from the World Ocean Elevation Data 5min grid.

Model validation

Figure 2 shows the comparisons between the buoy data and the outputs of the model which are forced by the reconstructed wind fields and NCEP/NCAR reanalysis wind fields. As shown in Figure 2a, the NCEP/NCAR reanalysis wind speeds at the site of the buoy are generally lower than the observations, especially during the periods of high wind speed. The correlation coefficient between them is about 0.65 (as shown in the Table 1). The corresponding SWHs from the model forced by the NCEP/NCAR reanalysis wind fields are also generally lower than the observations, especially during the periods of high wind speed. Their correlation coefficient reaches 0.73. To a great extent, the accuracy of the model output is dependent on the accuracy of the wind fields. We use the typhoon empirical model to reconstruct the wind fields in order to improve the accuracy of the wind fields during the typhoon periods. The correlation coefficient between the reconstructed wind speed and observations is 0.88, and it reaches 0.94 between the observed SWH and the SWH from the model forced by reconstructed wind fields (Figure 2b). So we use the 30-year reconstructed wind fields to drive the WW3 model to provide better data for the further study.

Figure 3a shows a map of SWH 26-year averaged anomaly over 1976–2001 in the SCS based on the ECMWF data (100º–122ºE, 0º–22ºN). The spatial distribution of SWHs anomalies presents sea basin structure. The SWHs more than 0.60 m mainly locate in north of 17°N, and east of 112°E, especially in the Luzon Strait where the SWHs anomalies are more than 0.80 m. The standard deviation (STD) of SWHs anomalies that more than 0.10m mainly distributes in the north of 10°N, east of 108°E, and the center of the high value is located in 118.5°E, 19°N. As shown in Figures 3c and d, the spatial distribution of annual mean SWHs anomalies and the STD of annual mean SWHs anomalies based on the WW3 model's outputs during 1976–2001 are roughly similar with that according to the ECMWF data during 1976–2001, but the model outputs of annual mean SWHs anomalies more than 0.60m just locate in the Luzon Strait. The area with STD more than 0.20 m is bigger than that according to the ECMWF data, but the high value center of the STD that calculated by the WW3 model's outputs is generally resemble as that according to the ECMWF data. The time series of the annual mean SWHs anomalies and annual mean wind speeds anomalies in the SCS are shown in Figure 3e. The correlation coefficient between them reaches 0.90. The trend of the SWHs anomalies according to the ECMWF data is roughly resemble as that based on the WW3 model's outputs, except the change between 1991 and 1993.

Interannual variability of significant wage height in the northern South China Sea

As the SWHs has remarkably interannual variability in the northeastern SCS and the tracks of typhoon through the SCS mainly locate north of 10ºN, the study area is restricted to the northern SCS (105º–122ºE, 10º–22ºN). In order to highlight the wave characteristics in the study area, we remove the influence of the Beibu Bay and Mindoro Strait due to the small standard deviation of the SWHs.

To discern the dominant spatial patterns and temporal coefficients of SWH in the northern SCS, the EOF analysis is applied to the SWHs anomalies data over 1976–2005. The first 5 modes decomposition by the EOF passed the significance test (>95% confidence level) and the cumulative variance contribution rate of the first 3 modes reaches 89.8%. The first mode of EOF accounts for 73.4% of the total variance. The variance contribution rates of the second and third modes are 11.2% and 5.2%, respectively. The variance contribution rates of the second and third modes are much smaller than that of the first mode. Therefore, we focus on the first mode of the SWH in this study.

Figures 4a and b show the temporal coefficient and spatial structure of the first mode, respectively. As shown in Figure 4b, the first mode presents a basin-scale variation in SWHs anomalies, with high value to the northwest Luzon Island. The high value center matches very well with the high STD area in Figure 3d, which indicates that the first mode explains the interannual variability of SWH to a great extent.

The power spectrum analysis of the PC-1 time series is shown in Figure 4c. The corresponding period of the maximum spectrum peak is 8 years and a slight year-to-year variability about 2.67 years is also found. Kako and Kubota (2006) and Sasaki et al. (2006) indicated that there were notable positive correlation between the SWH in the northern Pacific and El Niño events based on the T/P and ECMWF data. In view of the period of the El Niño events being about 2–7 years, we suppose that the first mode may be associated with El Niño events. As Figure 4a shows, during the periods of the strong El Niño events, such as during 1983–1984 and 1997–1998, the SWHs anomalies in the northern SCS are negative, while positive during 1988–1989 and 1999–2001 when La Niña occurred. The correlation coefficient between the time series of the PC-1 and the Niño3.4 index reaches -0.58, which reveals that the interannual variability of the SWH in the northern SCS has good correlation with the El Niño events. To a certain extent, the interannual variability of SWH in the northern SCS may be associated with the long-term climate change.

Many works have been focused on the wave climate in the Pacific, but the wave climate has less been studied in the SCS. The correlation coefficient between the wave height in the Pacific and El Niño events is positive (Sasaki et al., 2007), while the correlation coefficient between the wave height in the northern SCS and El Niño events is negative. The response to the El Niño events in the SCS for other variables such as the sea surface temperature (SST) and the response to the El Niño events in the Pacific are also anti-phase (Wang et al., 2006; Qiu et al., 2009; Mestas-Nunez et al., 2001). Wang et al. (2006) found that the interannual variability of the SST in the SCS is mainly affected by the El Niño events. The correlation coefficient between the PC-1 time series of SST in the northern SCS limited within deep-water area and Niño3.4 index was -0.71 (Qiu et al., 2009), while it was positive correlation between the SST anomaly in the equatorial eastern Pacific and El Niño events (Mestas-Nunez et al., 2001).

As shown in Figure 4a, the PC-1 is characterized by two prominent peaks that appeared in 1986 and 1999. According to the positive and negative values of the PC-1 time series, we divide the PC-1 time series into four periods for the further research: negative anomaly for 1978–1984 (period I), positive anomaly for 1985–1990 (period II), negative anomaly for 1991–1998 (period III) and positive anomaly for 1999–2005 (period IV).

As we know, the wind stress is a major factor to drive the wind wave. The time series of the zonal wind speed, meridional wind speed and wind speed averaged over the northern SCS all present in the Figure 5. The correlation coefficient between wind speed anomaly and the time series of the PC-1 is 0.56, with satisfies the 95% confidence level criterion with no phase difference. In addition, the wind stress anomaly has a correlation of -0.46 with the time series of the PC-1. Although the correlation coefficient between the zonal wind speed and the time series of the PC-1 during period 1976–2005 is 0.32, it reaches 0.73 during the period III. There is a good negative correlation between the meridional wind speed and the time series of the PC-1, the correlation coefficient during period 1976–2005 is -0.75 and it reaches -0.82 during the period II. As a result, we can say that the interannual variability of wind speed, the zonal wind speed, meridional wind speed and wind stress may support the interannual variability of SWH in the northern SCS.

The temporal relationship between the wind speed anomaly and the SWH anomaly is analyzed above, and now we will discuss the spatial relationship between them in the next part. The composite maps of the SWHs anomalies and wind speeds anomalies for the periods I-IV are shown in Figure 6. During the period I, negative anomalies of the SWHs in the northern SCS are notable, mainly located to the west of Luzon and southeast of Hainan Island and with clockwise wind speeds anomalies in the southern of the 18°N. During the period II, it presents distinct sea-basin distribution characteristics of the SWHs anomalies. The positive anomalies of the SWHs that located in the western of the Luzon are associated with anticlockwise wind speeds anomalies. During the period III, the isoline distribution of the SWHs anomalies are roughly extending from the southwestern to northeastern of the research area and parallel to the shoreline of the southeastern China. The negative anomalies of the SWHs mainly distribute in the northern of 16°N and positive anomalies in the southern of the 16°N, respectively. A clockwise wind field obviously locate in the negative anomalies area of the SWHs. Compared with the low values center of the negative anomalies of the SWHs during the period I, it is northward shifting from western of the Luzon to Luzon Strait during the period III. During the period IV, the SWHs anomalies in the research area are basically positive. The positive high values locate in the Luzon Strait, with a weak cyclonic wind field. Compared with the high values center of the positive anomalies of the SWHs during the period II, it is also northward shifting during the period IV.

Relationship between the interannual ariability of the significant wave heights and tropical cyclones activity

Graham and Diaz (2001) and Graham et al. (2002) clarified the long-term upward trend of SWH in the storm track as evidence of an increase in winter storm activity. Sasaki et al. (2005) also demonstrated that the recent increase of extreme wave heights in the western North Pacific corresponds to the recent increase in total duration of intense tropical cyclones. So we will discuss the interannual variability of SWHs anomalies in the northern SCS from the point of view of tropical cyclone activity in this section. Sasaki et al. (2007) used the tropical cyclone frequency and the total duration of tropical cyclones as the assessment index to analyze the relationship between the summertime wave height in western of the north Pacific and the tropical cyclones activity. The tropical cyclone frequency is calculated by summing the number of annual tropical cyclone with minimum central air pressure below 980hPa passing over the northern SCS. The total duration of the tropical cyclone is calculated by summing the duration of each tropical cyclone with minimum central air pressure below 980hPa passing over the northern SCS every year. Based on the Tropical Cyclone Best-Track Data which issued by the Regional Specialized Meteorological Center (RSMC) Tokyo Typhoon Center, we also utilize the two parameters as the assessment index to examine the relationship between the SWH anomaly in the northern SCS and tropical cyclone activities.

Figure 7 shows composite maps of the SLPs anomalies and ITC tracks for the periods I-IV. During periods I and III, positive SLPs anomalies are found in the northern SCS. In contrast, negative anomalies in the periods II excluded the Beibu Bay and the eastern of the Hainan Island and the period IV. As a result, the spatial distributions of the SLPs anomalies for the periods I-IV support the interannual variability of the SWHs anomalies in the northern SCS. But the SLPs anomalies and the number of typhoon track has no obvious positive or negative relationship. As the result shows, maybe the number of the typhoon is not the main reason to affect the SLPs, the frequency and the total duration of the typhoon are need to analysis.

The time series of the sea level pressure (SLP) and the time series of the PC-1 are shown in Figure 8a. The SLPs anomalies obtained from the NCEP/NCAR data in the northern SCS reveals distinct interannual variability. It has a correlation of -0.60 with the time series of the PC-1. The lower the SLPs, the greater the intensity of the typhoon, which means that wind speed is bigger, the SWHs is bigger. The time series of the PC-1, the intense tropical cyclone (ITC) frequency and the total duration of the ITC are shown in Figure 8b. During the periods I and III which show the negative anomalies of SWHs, the ITC frequency appears to be lower compared with the period II which shows the positive SWHs anomalies. The highest frequency of ITC is found during the period II that shows the largest positive anomalies of the SWHs, while the frequency of the ITC is least during the period IV. As Figure 8b shown, the total duration of ITC has the high peak in 1986 and the low peak in 2002. There is a good positive correlation between the total duration of the ITC and the time series of the PC-1 after 1999, the correlation coefficient reaches 0.72. The results reveal that the SWHs anomalies in the northern SCS are associated with ITC frequency during periods I-III, but the frequency of ITC cannot explain adequately the recent increase in the SWH. The increase of the SWHs anomalies in the northern SCS are due to the increase in the total duration of ITC after 1998.

Summary and conclusions

Although this region is generally covered by Sasaki et al. (2007) in a study that covered over 45 years, results for a semi-marginal sea such as the SCS are not clearly presented as his research was focused on Western North Pacific. Our area of interest is the South China Sea (SCS). By applying the EOF to analysis the SWHs from model hindcast in the northern SCS during 1976–2005 in this study, we have shown that the first EOF mode demonstrated the prominent interannual variability with maximum amplitude in the southwestern of the Luzon strait. To further analyze the time series of the PC-1, we can find significant periods of the SWH variability with 2.67 and 8 years in the northern SCS and a high negative correlation between the SWH in the northern SCS and El Niño events. El Niño Southern Oscillation (ENSO)-induced interannual variability in the SCS is documented by Liu et al. (2011), which supports this study. The zonal wind speeds anomalies, meridional wind speeds anomalies and SLPs anomalies during period 1976–2005 all also support the interannual variability of the SWHs anomalies in the northern SCS. The increase and decrease of the SWHs are associated with the frequency of TC during 1978–1998 and the increase of the SWHs in the northern SCS is due to the increase in the total duration of ITC after 1998.

Acknowledgements

We wish to thank Dr. Tolman at the National Weather Service for providing the WW3 model, the NOAA-CIRES Climate Diagnostics Center for providing NCEP/NCAR reanalysis wind fields and sea level pressure datasets, the ECMWF for the ERA-40 data. We are equally indebted to the Regional Specialized Meteorological Center (RSMC) Tokyo Typhoon Center for providing us with the Tropical Cyclone Best-Track Data. We specially wish to thank the South China Sea Branch of the State Oceanic Administration for providing us with the buoy data.

Funding

This work is supported by the Key Laboratory of Technology for Safeguarding of Maritime Rights and Interests and Application, SOA (No. SCS1601).

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References

Bacon, S., Carter, D.J.T.,
1991
.
Wave climate changes in the north Atlantic and North sea
.
Int. J. Climate
11
,
545
558
.
Cater, D.J.T., Draper, L.,
1988
.
Has the north-east Atlantic become rougher?
Nature
332
,
494
.
Chu, P.C., Cheng, K.F.,
2008
.
South China Sea wave characteristics during typhoon Muifa passage in winter 2004
.
J. Oceanogr.
64
,
1
21
.
Chu, P.C., Lu, S.H., Chen, Y.C.,
1997
.
Temporal and spatial variabilities of the South China Sea surface temperature anomaly
.
J. Geophys. Res.
102
(
C9
),
20937
20955
.
Graham, N.E., Diaz, H.F.,
2001
.
Evidence for intensification of North Pacific winter cyclones since 1948
.
Bull. Amer.Meteor. Soc.
82
,
1869
1893
.
Graham, N.E., Strange, R. R., Diaz, H.F.,
2002
.
Intensification of North Pacific winter cyclones 1948–98: Impacts on California wave climate
.
Proc.7th Int. Workshop on Wave Hindcasting and Forecasting
,
Banff, AB, Canada
.
U.S Army Engineer Research and Development Center
,
60
69
.
Holland, G.J.,
1980
.
An analytic model of the wind and pressure profiles in hurricanes
.
Mon. Wea. Rev.
108
,
421
427
.
Izaguirre, C., Menéndez, M., Camus, P., Losada, I. J.,
Exploring the interannual variability of extreme wave climate in the Northeast Atlantic Ocean
.
Ocean Modelling
59–60
(
12
),
31
40
.
Jiang, L.F., Zhang, Zh.X., Qi, Y.Q.,
2010
.
Simulations of WAVEWATCH III and SWAN in Northern South China Sea
.
Proceedings of the 20th International Offshore (Ocean) and Polar Engineering Conference
,
2010 June 14–18
,
Beijing
.
Kako, S., Kubota, M.,
2006
.
Relationship between an El Nino event and the interannual variability of significant wave heights in the North Pacific
.
Atmosphere-Ocean
44
,
377
395
.
Kalnay, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M., Saha, S., White, G., Woollen, J., Zhu, Y., Leetmaa, A., Reynolds, R., Chelliah, M., Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K.C., Ropelewski, C., Wang, J., Jenne, R., Joseph, D.,
1996
.
The NCEP/NCAR 40-year Reannalisis Project
.
Bull. Am. Meteorol. Soc.
77
(
3
),
437
471
.
Liu Q., Feng M., Wang D.,
2011
.
ENSO-induced interannual variability in the southeastern South China Sea
.
Journal of Oceanography
67
(
1
),
127
133
.
Mestas-Nunez, A.M., Enfield, D. B.,
2001
.
Eastern equatorial pacific sst variability: El Niño and Non- El Niño components and their climate associations
.
J. Climate
14
,
391
402
.
Osinowo, A., Lin, X., Zhao, D., Wang, Z.,
2016
.
Long-Term Variability of Extreme Significant Wave Height in the South China Sea
.
Advances in Meterology Vol.
2016
,
1
21
.
Qi, Y.Q., Shi, P.,
1999
.
Analysis on monthly average distribution characteristics of sea surface wind and wave in South China Sea using altimetry data
.
Tropical Oceanology
18
,
90
96
(
Abstract in English
).
Qi, Y.Q., Shi, P., Zhang, Z.X.,
2010
.
Calculation of Extreme Wind, Wave and Current in Deep Water of the South China Sea
.
International Journal of Offshore and Polar Engineering
20
(
1
),
18
23
.
Qiu, C.H., Jia, Y.L.,
2009
.
Seasonal and inter-annual variations of temperature and salinity in the northern South China Sea
.
Periodical of Ocean University of China
39
,
376
386
(
Abstract in English
).
Sasaki, W., Hibiya, T.,
2007
.
Interannual variability and Predictability of Summertime Significant Wave Heights in the Western North Pacific
.
J. Oceanogr.
63
,
203
213
.
Sasaki, W., Iwasaki, S. I., Matsuura, T., Iizuka, S.,
2005
.
Recent increase in summertime extreme wave heights in the western North Pacific
.
Geophys. Res. Lett.
32
,
1
4
.
Sasaki, W., Iwasaki, S. I., Matsuura, T., Lizuka, S.,
2006
.
Quasi-decadal variability of fall extreme wave heights in the western North Pacific
.
Geophys. Res. Lett.
33
(
9
),
179
212
.
Tolman, H.L.,
1989
.
The Numerical Model WAVEWATCH: A Third Generation Model for the Hindcasting of Wind Waves on Tides in Shelf Seas
.
Communication on Hydraulic and Geotechnical Engineering
,
Delhi University of Technology
,
89
2
.
Tolman, H.L.,
1991
.
A third-generation model for wind waves on slowly varying, unsteady and inhomogeneous depths and currents
.
J. Phys. Oceanogr.
21
,
782
797
.
Tolman, H.L.,
1992
.
Effects of Numerics on the Physics in a Third-Generation Wind-Wave Model[J]
.
Journal of Physical Oceanography
22
,
1095
1111
.
Tolman, H.L.,
2002
.
User manual and system documentation of WACEWATCH-III version 2.22
.
NOAA/NWS/NCEP Ocean Modeling Branch Contribution
166
,
110
.
Wang, C., Wang, W.Q., Wang, D.X., Wang, Q.,
2006
.
Interannual variability of the South China Sea associated with El Nino
.
J. Geophys. Res.
111
,
1
19
.
Wang, X.L L., Swail, V.R.,
2000
.
Changes of Extreme wave heights in northern hemisphere oceans and related atmospheric circulation regimes
.
J. Climate
14
,
2204
2221
.
WASA Group
,
1998
.
Changing waves and storms in the north east Atlantic? Bull
.
Amer. Meteor. Soc.
79
,
741
760
.
Weisse, R., Gunther, H.,
2007
.
Wave climate and long-term changes for the southern North Sea obtained from a high-resolution hindcast 1958–2002
.
Ocean Dynamics
57
,
161
172
.
Woolf, D.K., Challenor, P.G., Cottom, P.D.,
2002
.
Variability and predictability of the North Atlantic wave climate
.
J. Geophys. Res.
107
,
1
14
.