The focus of this study was the temporal and spatial variations of extreme significant wave heights and nearshore return-period wave heights in the South China Sea, based on the wave model and European Reanalysis-Interim data from 1979–2016. Measured buoy data were available from near Yongxing Island for comparison with the reanalysis data during the passage of typhoons. Annual maximum significant wave heights showed a statistically significant increasing trend over most of the South China Sea, whereas statistically insignificant decreasing or increasing trends were observed for seasonal maximum significant wave heights associated with the different characteristics of the typhoon events. Nonstationary generalized extreme value analysis was used to investigate the influence of nearshore extreme significant wave heights derived from the Simulating Waves Nearshore model at four offshore locations in the South China Sea. The fastest increase of 100-year return significant wave heights was found to be 0.0033 m yr−1 in the western South China Sea. The results show that, in recent decades, no significant variation trends can be found in return-period wave heights at nearshore of South China Sea, which may be related to tracks of intense typhoons in the region.

Introduction

Extreme (ocean surface) wave events in open oceans and coastal waters present danger to offshore platforms, shipping, fishing, and personal safety. Therefore, better understanding of extreme wave height is necessary for coastal management and maritime operations. The return period wave height is calculated as a standard for measuring the risk of extreme wave heights, but the question remains of how best to estimate return levels based on a measured time series of limited duration. The usual approach is to fit a probability distribution to the recorded data and to extrapolate it to the required return period. A basic assumption in such an approach is that the time series is stationary. However, if oceanographic wave climates change on decadal scales, then estimates of extreme values based on such analyses could be in error (Young et al., 2012). The paper deals with the analysis of the trends of the extreme wave climate in the South China Sea (SCS).

Many studies have used wave model reanalysis to examine trends extreme values of in significant wave height (SWH) (Young, 1999; Wang & Swail, 2001; Vinoth and Young, 2011; Young et al., 2012). For example, Rosenthal et al. (1998) found gradually rising trends in the North Atlantic for increasing extreme SWH values for 1955–1994 (0.3–0.4 m decade−1 for the 99th percentile). Based on altimeter data acquired over 18 years (1991–2008), Young et al. (2011) found trends becoming increasingly positive at the 99th-percentile values, but with a relatively neutral (0.07 m decade−1) global average trend. However, these results had low temporal and spatial resolutions for the SCS because of the low spatial resolution of the original data within the time series of the monthly mean wave height for 2° × 2° regions covering the globe. More recently, Izaguirre et al. (2013) studied SWH trends along the coasts of Central–South America using global reanalysis data. Their results showed a common positive trend in the Pacific basin throughout all seasons and a significant decreasing trend in the area of Suriname and to the north of Brazil (up to −1.5 cm yr−1 in March–May).

In the SCS, the return levels of SWH are associated with high surface wind speeds generated mainly by typhoons. The change of typhoons’ strength and track (Yang et al., 2015&2017) will affect the extreme SWHs’ spatial and temporal distribution. Changes in the intensities and tracks of typhoons in the SCS would lead directly to variation in the pattern of the extreme wave climate (Kumar et al., 2016). Some results have shown that global warming not only directly influences change in temperature but that it also enhances the frequency and intensity of typhoons (Webster et al., 2005). In general, two approaches are used to analyze nonstationary extreme variables; the partitioning statistical method and nonstationary extreme value theory (EVT). The former checks the trends of the return period values from different periods (Young et al., 2012; Vinoth and Young, 2011). In this method, as the length of the record decreases, the potential error (confidence interval) associated with the prediction increases. In nonstationary EVT, the parameters of the underlying distribution function are time-dependent. Alternative models may be used in this approach, such as polynomial trends, step changes, and trends on the scale or shape parameters (Katz, 2010; Cooley, 2009, 2013; Renard et al., 2013), which has led to the use of nonstationary EVT in a variety of fields (Cheng et al., 2014; Wang and Swail, 2006; Coles, 2001). Therefore, the nonstationary EVT approach with an annual maximum series (AMS) was adopted in this study.

In this study, the area selected in this study covered the entire SCS and the ocean east of the Philippines (5°S–32°N, 105°E–129°E) (Figure 1), because most typhoons that enter the SCS originate over the ocean to the east of the Philippines. Extreme SWH was taken as the annual/seasonal maximum SWH in the wave record from SWAN and European reanalysis (ERA). The remainder of this paper is organized as follows: The data set and methodology used in this study, and the details regarding the model setup and its validation, are all outlined in the next section. Analyses of the variability of the AMS and the relationship between the AMS and typhoon activity, together with a detailed discussion are next, followed by the trends of the return period values of coastal SWH. Finally, concluding statements are presented.

Data, models and methods of analysis

Wave model and input data

ERA-Interim

The present study was based on the global atmospheric reanalysis product of the ECMWF (European Centre for Medium-Range Weather Forecasts) known as ERA-Interim (Dee et al., 2011). ERA-Interim is the latest global reanalysis product of the ECMWF and it is available from 1979 onwards. Relative to the ERA-40 system, which was based on cycle 23r4 of the Integrated Forecasting System, ERA-Interim incorporates many important improvements, e.g. changes to the model resolution and physics, the use of four-dimensional variational assimilation, and various other changes in analysis methodology (Dee and Uppala, 2008, 2009). Based on improvements to the atmospheric model and assimilation procedures used in ERA-40, ERA-Interim uses a two-way coupled atmosphere–wave model system. An updated version of WAM includes a revised formulation of ocean wave dissipation, which has reduced the root mean square error in SWH against buoy data to below that in ERA-40 (Bidlot et al., 2007). Based on wave data measured at 9-m water depth over two years in the eastern Arabian Sea, Shanas and Kumar (2014a) found that ERA-Interim SWH data showed good correspondence with measured waverider buoy data. For the central Bay of Bengal, Shanas and Kumar (2014b) found that ERA-Interim SWH data showed good agreement with in situ buoy data during 2003, 2004, and 2005.

The present study used SWH data acquired over a 37-year period (1979–2016) at 6-h temporal and 0.25° × 0.25° spatial resolutions, which were downloaded directly from the ECMWF website (http://apps.ecmwf.int/datasets/, accessed April 1, 2017). The native horizontal resolution of this dataset is ∼80km (reduced Gaussian grid N128); that of ERA-Interim is ∼83km 0.75 deg−1. It is technically possible to achieve a higher resolution is technically possible, and the default interpolation method is bilinear for continuous parameters (e.g. Temperature) and nearest neighbour for discrete parameters (e.g. temperature). (https://software.ecmwf.int/wiki/display/CKB/ERA-interim%3A+What+is+the+spatial+reference). The low horizontal resolution may cause a decline in the available nearshore wave data in ERA-Interim dataset. Therefore, we obtained nearshore wave data from a high-resolution wave model.

Wave model

The SWAN is a third-generation wave model that was developed by Booij et al. (1999) for computing random, short-crested waves in coastal regions with islands, tidal flats, obstacles, and ambient currents. It has been used extensively to simulate waves in shallow water (Booij et al., 1999; Ris et al., 1999; Rogers et al., 2003), and it has recently been converted to run on unstructured meshes (Zijlema, 2010). The nested grid can be used for the high resolution data; thus SWAN is a viable option for use in our study.

The SWAN model solves the spectral action density balance equations for directional wavenumber spectra with full nonlinear physics. It accounts for wind input, wave–wave interaction, and dissipation associated with whitecap development and wave–bottom interaction. The SWAN model computes random, short-crested wind-generated waves in coastal regions and inland waters.
formula
(1)

From left to right, the terms on the left-hand side of the equation above represent the change of wave action over time, propagation of wave action in -space (with as the gradient operator in geographic space, the wave group velocity, and the ambient current vector), depth- and current-induced refraction, and approximate diffraction (with propagation velocity or turning rate ), and the change of σ due to variations in mean current and depth (with propagation velocity or shifting rate ) (Dietrich et al., 2011).

Wind fields/typhoon model

As is known, the annual extreme SWH, especially the SWH during typhoon passage, is the requirement for the return period values of SWH. In this study, for the return period SWH in coastal seas in the SCS, the Jelesnianski model (Jelesnianski, 1965) was adopted to produce the atmospheric pressure and wind fields of typhoons. The atmospheric pressure field is given by the following:

when
formula
(2)
and when
formula
(3)
where is the radius of the maximum wind speed from the typhoon center, which is represented by (Graham and Nunn, 1959)
formula
where is latitude and is the typhoon’s forward speed. Here, (=1013 hPa) is the environmental pressure far from the typhoon’s center and is its central pressure.

The above typhoon parameters were obtained from the Tropical Cyclone Best-Track Data, issued by the Regional Specialized Meteorological Center of the Tokyo Typhoon Center.

Data and model validation

A wave buoy located at W1 (Figure 1) provided SWHs, determined by a pressure sensor, which were used to validate the ERA-Interim SWHs. The pressure data were recorded continuously at a rate of 1 Hz for 10 min, and the data for every 30 min were processed as one record. Wave data were acquired only during certain typhoons because of both the devastating power of the typhoons and the difficulty of maintenance. Figure 2 shows that the SWHs captured by the wave buoy for six typhoons that passed near W1 match the SWAN model data well.

In the SWAN model, the gridded bathymetry of the study domain was extracted from the GEBCO (General Bathymetric Chart of the Oceans, http://www.gebco.net) database. The GEBCO is a global 30-arcsecond grid generated through combinations of quality-controlled depth-sounding survey data blended with satellite-derived gravity data. A comparison of the SWHs obtained from the ERA-interim, SWAN model, and buoy observations is presented in Figure 2.

For the trend of extreme SWH, high-resolution data sets of typhoon wind fields during 1949–2005/2008 were employed to drive the SWAN spectral wave model to derive the maximum SWHs during the typhoon processes.

In the study, only the maxima of typhoon SWHs from the ERA-Interim and SWAN model could be used for extreme analyses; therefore, the focus was on the maximum SWHs during typhoons. The good correspondence of the ERA-Interim and SWAN model with the measured wave buoy data is shown in Figure 3. Because its grid is finer than the ERA-Interim, the match of the SWAN model with the measured wave buoy data is the closest.

Nonstationary approach

Nonstationary generalized extreme value (GEV) distributions are generally used to fit the AMS, the structure of which is described as follows:
formula
(5)
where denotes the GEV distribution with the probability distribution function:
formula
(6)
defined as where the notation and represent the location, scale, and shape parameters, respectively, all of which are functions of time Here, by keeping the scale and shape parameters constant, the location parameter is assumed a linear function of time to account for nonstationarity (Eq. 7)
formula
(7)
where t is the time (in years), and are the parameters.
The concept of return period can also be extended to a non-stationary framework (e.g. Rootzén and Katz 2013; Cheng et al. (2014); Salas and Obeysekera 2013). Nonstationary GEV distributions can be described as follows:
formula
formula
where T is the return period.

Cheng et al. (2014) developed a software package called Nonstationary Extreme Value Analysis (NEVA). NEVA uses a Bayesian technique to infer the GEV distribution parameters under stationary and nonstationary conditions. The Bayesian-based Markov chain Monte Carlo approach for obtaining a posteriori distributions of parameters from an arbitrary distribution has become increasingly popular and it has been used in several studies of extremes. Both the sensitivity analyses of parameters and the significance level in NEVA can show significant performances in this article.

Variability of annual maximum significant wave height in South China Sea

Long-Term Trend

In terms of the long-term trends of annual maximum SWH (Figure 4), positive trends of 1.0–7.8 mm yr−1 dominate most of the study area. The trends are particularly strong (>7.0 mm yr−1) around the Luzon Strait. Insignificant and decreasing trends (<0.0 mm yr−1) are observed in the northwest China Sea, Taiwan Strait, and south of the Philippines.

The trends of seasonal maximum SWHs calculated for winter (December–February; DJF), spring (March–May; MAM), summer (June–August; JJA), and fall (September–November; SON) are shown in Figure 5. In winter, most areas have obvious increasing positive trends of SWH, the rates of growth of which are faster than in the other three seasons. Areas with the largest increasing trends are mainly distributed around the Luzon Strait (9.0–11.5 mm yr−1). The pattern is similar in spring but with most areas exhibiting insignificant trends (1.0–8.1 mm yr−1) in SWH. The area with the largest increasing trends extends into the waters further south of the Luzon Strait. During summer, northern waters exhibit positive trends of SWH (1.0–7.1 mm yr−1), while negative trends (−3.9 to 1.0 mm yr−1) are observed in the waters between Vietnam and Palawan. During fall, insignificant positive trends dominate most areas; however, negative trends (−3.7 to 0.0 mm yr−1) are observed mainly in the coastal area of southern China and the Taiwan Strait

Figure 6 shows the temporal trends in annual and seasonal mean maximum SWHs. Figure 6(a) shows an increase of 0.0065 m yr−1 for mean annual maximum SWH throughout the 38-year period. Figure 6(b) shows increases in SWH of 0.0091, 0.0114, 0.00409, and −0.00028 m yr−1 in winter, spring, summer, and fall, respectively.

During the entire study period, the main long-term trends of annual maximum SWH are positive throughout the study area. Seasonally, winter and spring exhibit positive trends of maximum SWH. During summer, the mean seasonal maximum SWHs in all areas have insignificant positive trends, except for long-term negative trends in southern parts of the study area. Conversely, although the trends of maximum SWH in most areas have insignificant positive trends during fall, the seasonal maximum SWH of all areas has a negative trend (Figure 6 (b)).

The seasonal and annual trends are similar to those found by Osinowo et al. (2016), in which the long-term (1976-2005) variability of the 99th-percentile of SWH from the WW3 wave model for the SCS (95°E ∼135°E, 5°S ∼30°N) was analyzed. Although there are some differences in the study area and duration of the period analyzed, this still suggests that our conclusion is reliable and that ERA-Interim data can be used to analyze long-term trends in annual maximum SWHs.

Relationship between interannual variability of significant wave heights and typhoon activity

Intense typhoons are a major factor in driving extreme wind waves in the SCS. Figure 7 shows the trends of the numbers (Category: >5 in the Tropical Cyclone Best-Track Data) and the annual minimum central pressures of typhoons within the study area are both negative, i.e.: −0.03 yr−1, and −0.433 hPa yr−1, respectively. This supports the assertion that the numbers of intense typhoons are declining but that their intensities are increasing year by year in the western Pacific Ocean (Webster et al., 2005). Lower minimum central pressure reflects greater typhoon intensity, which means stronger wind speeds and higher SWHs.

Figure 8 presents the spatial pattern of the empirical orthogonal function (EOF) 1 in the four seasons (color shading) and the 80% quantile of the EOF1 value (green line). The spatial patterns of the EOF1 in DJF and MAM are similar and are characterized by two prominent positive peaks. For SON, EOF1 exhibits a double-peaked pattern, although the peak in the SCS is the weaker of the two. The spatial pattern of the EOF1 in JJA is unimodal with the peak northeast of the Philippines.

Based on the Tropical Cyclone Best-Track Data issued by the Regional Specialized Meteorological Center of the Tokyo Typhoon Center, we also used the passing rate as an assessment index with which to examine the relationship between SWH and tropical cyclone activity. The tropical cyclone passing rate is calculated by summing the number of tropical cyclones with minimum central air pressure <980 hPa. In this study, these values are 8/14, 13/15, 71/110, and 62/136 for DJF, MAM, JJA, and SON, respectively. Although fewer intense typhoons occurred in DJF and MAM, the contour line of the 80% quantile of the EOF1 value surrounds the track of almost all intense typhoons. Thus, we can say that the maximum SWH spatial pattern of EOF1 may be determined by the characteristics of intense typhoons within the study area.

Long-term trends of nearshore extreme significant wave heights

The return period level of SWH in offshore waters is important for offshore platforms, shipping, fishing, and personal safety. Because of the anticipated increase in human activities in the SCS, this study examined the influence of extreme SWHs on offshore waters using four long-term SWH data-sets, obtained from SWAN typhoon hindcasts (Table 1). It focused on four locations of interest (A, B, C, and D in Figure 1) that are highly populated areas with developed economies.

With NEVA, the trend of the return level is related to the number of simulations. A trial experiment revealed that when the number of simulations was 30,000, the trend of the return level with time was stable, and the variant rate of the slope of the 100-year return level with time was within 5%. The details of the data are displayed in Table 1. The dot-dash lines in Figure 9 denote the SWH return levels for 100-, 50-, 25-, 10-, and 2-year return periods from 1949-2055 at locations A, B, C, and D. The results shows that extreme SWHs at points B and D have increased since 1949, but that the rate of increase is slow (≤0.0033 m/yr). For locations A and C, the return SWHs show negative trends (−0.006 and −0.0015 m yr−1, respectively). Four points off the shore of the SCS exhibit small or no significant trends for the 100-year return levels.

Location A is approximately 500m southeast of the coast on the island of Hainan. Table 2 shows that the 100-year return SWH at location A is 5.5484 m for 2020 and that this decreases to 5.3649 m by 2050. In other words, the 100-return SWH will be decline with the decrease in return levels, with a predictable trend. However, at location B in the west of the SCS, the 100-year return SWH will increase from 10.6791 m in 2020 to 10.7778 m in 2050.

The results show that the spatial distribution of trends in the return levels of SWHs off the shore of the SCS do not follow any obvious laws. This may be because SWHs are affected by the cumulative effects of many factors, including topography, extreme weather conditions, and typhoon tracks. However, we have determined that under climate change, the return levels of SWHs off the shore of the SCS exhibit small or no significant trends.

Summary and conclusions

Annual maximum wave processes are nonstationary because of climate change. This paper analyzed extreme SWHs in the SCS and modeled extreme SWH using the nonstationary GEV approach.

It was established that analysis of the ERA-Interim SWH data could reveal the statistical characteristics of the AMS of SWHs. Apart from waters sheltered by islands, the annual maximum SWH in the SCS shows a rising trend. Areas with the largest increasing trends are distributed mainly near the Luzon Strait (9.0–11.5 mm yr−1). In winter and spring, the rate of growth of the maximum SWH is faster than in summer. The maximum SWH in fall shows a declining trend.

Comparison of the EOF1 pattern and typhoon activity showed that the most intense typhoons passed through the area enclosed by the 80% quantile of the EOF1 value. Therefore, we can say that the maximum SWH spatial pattern of EOF1 might be determined by the tracks of intense typhoons within the study area. In the coastal area, the trend of the SWH return level, driven by the high-resolution SWAN model, was investigated for four locations. Insignificant decreasing or increasing trends were found in the coastal areas of the SCS, and among them, the fastest increase of 100-year return SWH was found to be 0.0033 m yr−1 in the western SCS.

Acknowledgements

We are indebted equally to the Regional Specialized Meteorological Center of the Tokyo Typhoon Center for providing the Tropical Cyclone Best-Track Data, and to the ECMWF for providing the ERA-Interim reanalysis data. This work is supported by the Major State Research Development Program of China (2016YFC1402603), and the International Partnership Program of the Chinese Academy of Sciences (Grant no. 131551KYSB20160002).

Note

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uaem.

The text of this article is only available as a PDF.

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