Wave climate change analysis based on long time-series buoy data

Using the buoy dataset from 2011 to 2022, the trend of wave climate change was analyzed at DaChen station located in the Taizhou City, Zhejiang Province. The results show a decreasing trend of the maximum significant wave height (Hs). Whereas the wave height is higher than 4 m, the corresponding wave period is in the range of 8-14s. Disastrous waves mainly occur between July and October. The relevant analysis presents the wave characteristics at the DaChen station, which is helpful for protecting the life safety along the coast and providing references for offshore engineering design.


Introduction
The China Sea is the sea passage between China and the world, and is significant in economic and military strategies.With the implementation and improvement of China's various marine policies, especially the "Belt and Road" strategy, more and more people have been involved in the marine business.Elucidating the spatial and temporal characteristics of wave distribution and change rules is conducive to safeguarding the navigation safety of ships in the sea area and the people's lives and properties in the coastal region.
Scholars have already studied the wave characteristics of the China Sea by using long-term wave data.Xu et al [1] simulated the wave field of China's offshore from 1979 to 2018 based on TOMAWAC, and statistically calculated the spatial distribution of wave extremes for one in many years.Liu et al [2] used ERA-20C reanalysis data to statistic the change trend of the wave in the Chinese offshore, and there is a decreasing trend of the wave height in the Bohai Sea while an increasing trend of the wave height in the South China Sea.Yi et al. [3] statistically investigated the long-term wave characteristics in the South China Sea based on the ERA-Interim dataset, and found that the effective wave height in the South China Sea increasing at a rate of 0.2-0.8cm/a during 1979-2015.Dong et al. [4] conducted a wave hindcast simulation over a 40-year period, and the results showed that the effective wave height and the averaging period of the Yellow Sea gradually increased and decreased from the south to the north.He et al. [5] constructed a high-precision wave field in the East China Sea using a highresolution wind speed data-driven wave model, and explored the spatial distribution pattern of extreme wave heights in the East China Sea, which gradually increased from offshore to far offshore and the extreme value appeared in the northeast of Taiwan Island.Wang et al. [6] analysed the ERA5 wave data and showed that the extreme waves in the southern part of the East China Sea significantly enhanced, with an amplitude of +5 cm/a.Feng et al. [7] investigated the long-term changes of typhoon waves in Zhejiang and Fujian based on wave hindcast simulations, and found that there was an increasing tendency for the extreme values of typhoon waves in the northern part of Fujian Sea, with a maximum value of 0.05 m/a.Wang et al. [8] used the ERA-Interim data in 40 years to investigate the spatial distribution pattern of extreme wave heights in the East China Sea, and the extreme values appeared in the northeast of Taiwan Island.Wang et al. [8] used 40 years of ERA-Interim data to study the spatial and temporal characteristics of the waves in Beibu Gulf, and found that the wind speed has a decrasing tendency, but the wave height increases as a whole.Due to the complexity of wave characteristics in the Chinese offshore, the nearshore numerical simulation is inaccurate.Buoy is a main method to analyses the nearshore wave characteristics.Based on the background mentioned above, this paper analyses the wave climate trends at Da Chen (referred to as DCN) stations located along the coast of Zhejiang Province by using the buoy dataset from 2011 to 2022.

Wave observation station data
The wind and wave data for this study is observed from one station offshore China, namely DCN, provided by the National Marine Data and Information Service (NMDIS) of China.The spatial distribution of the station is given in Figure 1.The station is located in the offshore area and is distributed in the East China Sea, which is representative and typical in the China offshore.Table 1 gives the specific information of the station, with an observation spanning range of more than 12 years, which is chronic and continuous in time.Since 2011, the temporal resolution of data recording has been increased to 1h, with 24 observations per day in the DCN observation.The major categories of wave parameters recorded mainly include: Significant wave height Hs and its corresponding period Ts, and the main wind elements recordeds: wind speed and wind direction at 10m height.

Mann-Kendall test
The Mann-Kendall test is a non-parametric test of randomness against trend, which generally used in hydrological and meteorological datasets to detect monotonic trends.For a null hypothesis of randomness, H0, the wave height/wave period data in time series [X=(x1, x2, …, xn)] is n independent and identically distributed random samples.The alternative hypothesis, H1, the test for trend is twosided.
Based on the null hypothesis H0, there is no trend.The test statistic, S can be defined as given in Eq.( 1), ( ) where n is the number of data points and sgn is the sign function which can be defined as given in Eq.( 2), ( ) ) n is the number of the data, xi and xj are the data at moments i and j respectively.
For the assumption of the null hypothesis, S is symmetric and normally distributed, with a mean of zero and variance given in Eq. ( 3): Given the variance Var(S), the standardized test statistic, Z, can be calculated as follows: 1 for 0 Var( ) Typically, a two-sided test is then performed by comparing the Z to the α/2 percentage point of a standard normal distribution.For a given significance level, the null hypothesis, is unacceptable, that is, there is a statistically significant trend if |Z|≥Z1−a/2.A positive/ negative value of Z indicates an increasing/decreasing trend at the chosen significance level.The DCN station wave height trend is verified by the MK trend test.

Trends in wave parameters
The long-term change characteristics of waves are of great significance in deepening the understanding of the ocean dynamic environment and the development and utilization of marine energy [9].In order to analyze the long-term change of wave height, the yearly Hs maxima of the DCN buoys for 12 years were calculated, and then a linear function was fitted to the series of Hs annual maxima.Figure2 gives the magnitude of the variation of Hs annual maxima of DCN, and it can be seen from the figure that, the Hs annual maxima of the station shows a significant decreasing trend to -0.14 m/year.However, due to the time span of the observational data of 12 years, the trend of the variation of the Hs maximum wave height is more affected by the sudden climatic changes.However, since the time span of the observed data is only 12 years, the variation trend of the maximum wave height of Hs is greatly affected by the sudden climate change.Therefore, in order to obtain a reasonable value for the trend of the Hs maxima at this station, it is necessary to analyze the data over a longer time span.Hs is mainly distributed between 0.5 m and 1.5 m, accounting for 90.56%.The frequency of occurrence near 0.5 m~1.0 m and 1.0 m~1.5 m is higher, which is 40.36% and 35.94% respectively.The frequency of occurrence higher than 3m was lower than 1.32%.Ts were mainly distributed between 4~8s, accounting for 84.11%.Among them, 6s to 8s appeared with the highest frequency of 57.90%.The frequency of occurrence of longer period waves greater than 8s is less than 15.81%.To further understand the distribution characteristics of Hs and its corresponding Ts, the joint Hs-Ts distribution was plotted.The distribution shows an upper triangular feature as can be seen from Figure 4.When the wave height is in the interval of 0~1m, the corresponding wave period is in the range of 3s~14s; when the wave height is in the range of 2~3m, the corresponding wave period mainly concentrates in the range of 5s~13s; and when the wave height is larger than 4m, the corresponding wave period is in the range of 8~14s.In conclusion, the wave characteristics of the DCN stations are that the larger the wave height, the larger the wave period.From the geographical location of the station in Figure 1, it is possible that the long-period waves propagate from the East China Sea and arrive at the DCN station as swell with larger wave energy.To confirm that the waves with larger wave heights propagate from the East China Sea, a probabilistic rose diagram of wind direction and wind speed at the DCN station was plotted (Figure 5).Combined with the geographic location, it can be seen from the plot that the winds at this station are mainly in the N direction and NNE direction.These two wind directions are mainly offshore winds, and since the buoy is located in the near-shore area, according to the fetch-law of wind-generated waves, it is difficult to generate waves with larger wave heights and longer wave periods with limited fetch.In addition, for further illustration, the wind and wave correlation coefficients for this station are discussed below.

Wind and wave correlation
The studies mentiond above revealed that the variation in wave height were associated with the change in wind over the area.
Wind is the main disturbance and driver of waves.Generally speaking, the changes in waves are a consequence of variations in the wind.When assessing the dynamics of long-term changes in waves, the influence of wind may be considered first.A correlation analysis method to reflect the extent to that wind affected the waves.
The Pearson correlation coefficient was chosen as a statistical indicator.The correlation between the wind and wave fields was presented by calculating the correlation coefficient R between wave height and wind speed.In addition, all of the above are passed the t-test.
The wind-wave correlation coefficient of DCN station was calculated, and the result was 0.54, which indicated that the wind-wave correlation of this station was low, and the waves with long period and large wave energy might be propagated from the distant sea.7 is tropical cyclones.The main characteristics of catastrophic waves in this area are large wave heights and long wave periods.Therefore, when engaging in marine operations in this area, it is important to pay attention not only to the impact damage to structures caused by large wave energy, but also the resonance damage caused by low-frequency waves that are close to the intrinsic frequency of structures.

Conclusions
The wind and wave characteristics of DCN stations from 2011 to 2022 are analyzed by using the buoy station dataset, and the following conclusions are obtained: The annual trend of Hs maxima at DCN stations shows a decreasing trend.The Hs and Ts of DCN shows a single-peak distribution, with Hs mainly distributed between 0.5m and 1.5m, accounting for 90.56%, and Ts occurring most frequently between 6s and 8s, reaching 57.90%.Overall, the waves at DCN stations are characterized by the fact that the larger the wave height, the larger the wave period.Catastrophic waves mainly occur from July to October, corresponding to the period of tropical cyclone prevalence in the Northwest Pacific Ocean.

Figure 1 .
Figure 1.Wave observation point around China

Figure 2 .
Figure 2. Linear trend of the maximum value of Hs.

Figure 3 .
Figure 3. Histogram of the distribution characteristics of Hs and Ts.Figure 3 statistically shows the distribution probability of Hs and Ts of DCN buoys during the period from 2011 to 2022.As shown in the figure, Hs and Ts of DCN have a single-peaked distribution.Hs is mainly distributed between 0.5 m and 1.5 m, accounting for 90.56%.The frequency of occurrence near 0.5 m~1.0 m and 1.0 m~1.5 m is higher, which is 40.36% and 35.94% respectively.The frequency of occurrence higher than 3m was lower than 1.32%.Ts were mainly distributed between 4~8s, accounting for 84.11%.Among them, 6s to 8s appeared with the highest frequency of 57.90%.The frequency of occurrence of longer period waves greater than 8s is less than 15.81%.

Figure 3
Figure 3. Histogram of the distribution characteristics of Hs and Ts.Figure 3 statistically shows the distribution probability of Hs and Ts of DCN buoys during the period from 2011 to 2022.As shown in the figure, Hs and Ts of DCN have a single-peaked distribution.Hs is mainly distributed between 0.5 m and 1.5 m, accounting for 90.56%.The frequency of occurrence near 0.5 m~1.0 m and 1.0 m~1.5 m is higher, which is 40.36% and 35.94% respectively.The frequency of occurrence higher than 3m was lower than 1.32%.Ts were mainly distributed between 4~8s, accounting for 84.11%.Among them, 6s to 8s appeared with the highest frequency of 57.90%.The frequency of occurrence of longer period waves greater than 8s is less than 15.81%.

Figure 4 .
Figure 4. Hs-Ts joint distribution.To further understand the distribution characteristics of Hs and its corresponding Ts, the joint Hs-Ts distribution was plotted.The distribution shows an upper triangular feature as can be seen from Figure4.When the wave height is in the interval of 0~1m, the corresponding wave period is in the range of 3s~14s; when the wave height is in the range of 2~3m, the corresponding wave period mainly concentrates in the range of 5s~13s; and when the wave height is larger than 4m, the corresponding wave period is in the range of 8~14s.In conclusion, the wave characteristics of the DCN stations are that the larger the wave height, the larger the wave period.From the geographical location of the station in Figure1, it is possible that the long-period waves propagate from the East China Sea and arrive at the DCN station as swell with larger wave energy.

Figure 5 .
Figure 5. Rose diagram of wind direction and speed.

Figure 6 .
Figure 6.Characteristics of the monthly distribution of the number of occurrences of Hs ≥ 3m from 2011 to 2022.In ocean engineering, waves with Hs ≥ 3 m are often regarded as catastrophic waves.We counted the number of occurrences of catastrophic waves at DCN stations during the period from 2011 to 2022, as shown in Figure.6.It can be seen from the figure that catastrophic waves mainly occur from July to October, which corresponds to the period of tropical cyclone prevalence in the Northwest Pacific Ocean.Among them, the month of August recorded the highest number, with a cumulative total of 293 occurrences.Combined with the aforementioned, the main cause of catastrophic waves in this area

Table 1 .
Details of moored buoys