Estimation of Design Wave Heights for Coastal Sea Areas

Based on historical wind fields in the Bohai Sea, a sequence of annual extremal wave heights is produced with numerical wave models for deep-water and shallow water. The design wave heights with different return periods for the nearest deep-water point and for the shallow water point are estimated on the basis of P-III type, Weibull distribution, and Gumbel distribution; and the corresponding values for the shallow water point are also estimated based on the HISWA model with the input of design wave heights for the nearest deep-water point. Comparisons between design wave heights for the shallow water point estimated on the basis of both distribution functions are HISWA model show that the results from different distribution functions scatter considerably, and influenced strongly by return periods; however, the results from the HISWA model are convergent, that is, the influence of the design wave heights estimated with different distribution functions for deep water is weakened, and the estimated values decrease for long return periods and increase for short return periods. Therefore, the numerical wave model gives a more stable result in shallow water design wave estimation because of the consideration of the effect of physical processes which occur in shallow water.

Long-Period Distribution of Wave Heights and Its Application

This paper reveals that the long-period statistic distribution of the characteristic heights of deep-water waves assumes the lognormal distribution. Thereafter, the largest wave-height which may occur in the service life of coastal structures is derived in this paper.

Effect of wave spectrum width on the probability density distribution of wind-wave heights

The probability distribution of wave heights under the assumption of narrowband linear wave theory follows the Rayleigh distribution and the statistical relationships between some characteristic wave heights, derived from this distribution, are widely used for the treatment of realistic wind waves. However, the bandwidth of wave frequency influences the probability distribution of wave heights. In this paper, a wave-spectrum-width parameter B was introduced into the JONSWAP spectrum. This facilitated the construction of a wind-wave spectrum and the reconstruction of wind-wave time series for various growth stages, based on which the probability density distributions of the wind-wave heights were studied statistically. The distribution curves deviated slightly from the theoretical Rayleigh distribution with increasing B. The probability that a wave height exceeded a certain value was clearly smaller than the theoretical value for B≥0.3, and the difference between them increased with the threshold value. The relation between the Hs/σ ratio and B was investigated statistically, which revealed that the Hs/σ ratio deviated from 4.005 and declined with B. When B reached 0.698 1, the Hs/σ ratio was 3.825, which is about 95.5% of its original value. This indicates an overestimation in the a potential method for improving the accuracy of the Hs extremely large waves under severe sea states. prediction of Hs from Hs=4.005σ, and provides remote sensing retrieval algorithm, critical for

The validation of the significant wave height product of HY-2altimeter–primary results

The HY-2 satellite was successfully launched on 16 August 2011. The HY-2 significant wave height （SWH） is validated by the data from the South China Sea （SCS） field experiment, National Data Buoy Center （NDBC/ buoys and Jason-1/2 altimeters, and is corrected using a linear regression with in-situ measurements. Com- pared with NDBC SWH, the HY-2 SWH show a RMS of 0.36 m, which is similar to Jason- 1 and Jason-2 SWH with the RMS of 0.35 m and 0.37 m respectively; the RMS of corrected HY-2 SWH is 0.27 m, similar to 0.27 m and 0.23 m of corrected Jason-1 and Jason-2 SWH. Therefore the accuracy of HY-2 SWH products is close to that of Jason-1/2 SWH, and the linear regression function derived can improve the accuracy of HY-2 SWH products.

The validation of HY-2 altimeter measurements of a significant wave height based on buoy data

HY-2 has been launched by China on August 16, 2011 which assembles multi-microwave remote sensing payloads in a body and has the ability of monitoring ocean dynamic environments. The HY-2 satellite data need to be calibrated and validated before being put into use. Based on the in-situ buoys from the Nation- al Data Buoy Center （NDBC）, Ku-band significant wave heights （SWH, hs） of HY-2 altimeter are validated. Eleven months of HY-2 altimeter Level 2 products data are chose from October 1, 2011 to August 29, 2012. Using NDBC 60 buoys yield 902 collocations for HY-2 by adopting collocation criteria of 30 min for tempo- ral window and 50 km for a spatial window. An overall RMS difference of the SWH between HY-2 and buoy data is 0.297 m. A correlation coefficient between these is 0.964. An ordinary least squares （OLS） regression is performed with the buoy data as an independent variable and the altimeter data as a dependent vari- able. The regression equation of hs is hs （HY-2）=0.891 × hs （NDBC）＋0.022. In addition, 2016 collocations are matched with temporal window of 30 rain at the crossing points of HY-2 and Jason-2 orbits. RMS difference of Ku-band SWH between the two data sets is 0.452 m.

Validation of Chinese HY-2 satellite radar altimeter significant wave height

Chinese Haiyang-2（HY-2） satellite is the first Chinese marine dynamic environment satellite. The dual-frequency （Ku and C band） radar altimeter onboard HY-2 has been working effective to provide operational significant wave height （SWH） for more than three years （October 1, 2011 to present）.We validated along-track Ku-band SWH data of HY-2 satellite against National Data Buoy Center （NDBC） in-situ measurements over a time period of three years from October 1, 2011 to September 30, 2014, the root mean square error （RMSE） and mean bias of HY-2 SWH is 0.38 m and （-0.13±0.35） m, respectively. We also did cross validation against Jason-2 altimeter SWH data, the RMSE and the mean bias is 0.36m and （-0.22±0.28） m, respectively. In order to compare the statistical results between HY-2 and Jason-2 satellite SWH data, we validated the Jason-2 satellite radar altimeter along-track Ku-band SWH data against NDBC measurements using the same method. The results demonstrate the validation method in this study is scientific and the RMSE and mean bias of Jason-2 SWH data is 0.26 m and （0.00±0.26） m, respectively. We also validated both HY-2 and Jason-2 SWH data every month, the mean bias of Jason-2 SWH data almost equaled to zero all the time, while the mean bias of HY-2 SWH data was no less than -0.31m before April 2013 and dropped to zero after that time. These results indicate that the statistical results for HY-2 altimeter SWH are reliable and HY-2 altimeter along-track SWH data were steady and of high quality in the last three years. The results also indicate that HY-2 SWH data have greatly been improved and have the same accuracy with Jason-2 SWH data after April, 2013. SWH data provided by HY-2 satellite radar altimeter are useful and acceptable for ocean operational applications.

A semiempirical algorithm for SAR wave height retrieval and its validation using Envisat ASAR wave mode data

Many synthetic aperture radar (SAR) wave height retrieval algorithms have been developed.However,the wave height retrievals from most existing methods either depend on other input as the first guess or are restricted to the long wave regime.A semiempirical algorithm is presented,which has the objective to estimate the wave height from SAR imagery without any prior knowledge.The proposed novel algorithm was developed based on the theoretical SAR ocean wave imaging mechanism and the empirical relation between two types of wave period.The dependency of the proposed model on radar incident and wave direction was analyzed.For Envisat advanced synthetic aperture radar (ASAR) wave mode data,the model can be reduced to the simple form with two input parameters,i.e.,the cutoff wavelength and peak wavelength of ocean wave,which can be retrieved from SAR imagery without any prior knowledge of wind or wave.Using Envisat ASAR wave mode data and the collocated buoy measurements from NDBC,the scmicmpirical algorithm is validated and compared with the Envisat ASAR level 2 products.The root-mean-square-error (RMSE) and scatter index (SI) in respect to the in situ measurements are 0.52 m and 19％ respectively.Validation results indicate that,for Envisat ASAR wave mode data,the proposed method works well.

Wave height measurement in the Taiwan Strait with a portable high frequency surface wave radar

As an important equipment for sea state remote sensing, high frequency surface wave radar （HFSWR） has received more and more attention. The conventional method for wave height inversion is based on the ratio of the integration of the second-order spectral continuum to that of the first-order region, where the strong external noise and the incorrect delineation of the first- and second-order Doppler spectral regions due to spectral aliasing are two major sources of errors in the wave height. To account for these factors, two more indices are introduced to the wave height estimation, i.e., the ratio of the maximum power of the second-or- der continuum to that of the Bragg spectral region （RSCB） and the ratio of the power of the second harmonic peak to that of the Bragg peak （RSHB）. Both indices also have a strong correlation with the underlying wave height. On the basis of all these indices an empirical model is proposed to estimate the wave height. This method has been used in a three-months long experiment of the ocean state measuring and analyzing ra- dar, type S （OSMAR-S）, which is a portable HFSWR with compact cross-loop/monopole receive antennas developed by Wuhan University since 2006. During the experiment in the Taiwan Strait, the significant wave height varied from 0 to 5 m. The significant wave heights estimated by the OSMAR-S correlate well with the data provided by the Oceanweather Inc. for comparison, with a correlation coefficient of 0.74 and a root mean square error （RMSE） of 0.77 m. The proposed method has made an effective improvement to the wave height estimation and thus a further step toward operational use of the OSMAR-S in the wave height extraction.

Estimating significant wave height from SAR imagery based on an SVM regression model

A new method for estimating significant wave height（SWH） from advanced synthetic aperture radar（ASAR） wave mode data based on a support vector machine（SVM） regression model is presented. The model is established based on a nonlinear relationship between σ0, the variance of the normalized SAR image, SAR image spectrum spectral decomposition parameters and ocean wave SWH. The feature parameters of the SAR images are the input parameters of the SVM regression model, and the SWH provided by the European Centre for Medium-range Weather Forecasts（ECMWF） is the output parameter. On the basis of ASAR matching data set, a particle swarm optimization（PSO） algorithm is used to optimize the input kernel parameters of the SVM regression model and to establish the SVM model. The SWH estimation results yielded by this model are compared with the ECMWF reanalysis data and the buoy data. The RMSE values of the SWH are 0.34 and 0.48 m, and the correlation coefficient is 0.94 and 0.81, respectively. The results show that the SVM regression model is an effective method for estimating the SWH from the SAR data. The advantage of this model is that SAR data may serve as an independent data source for retrieving the SWH, which can avoid the complicated solution process associated with wave spectra.

The difference between the joint probability distributions of apparent wave heights and periods and individual wave heights and periods

The joint distribution of wave heights and periods of individual waves is usually approximated by the joint distribution of apparent wave heights and periods. However there is difference between them. This difference is addressed and the theoretical joint distributions of apparent wave heights and periods due to Longuet-Higgins and Sun are modified to give more reasonable representations of the joint distribution of wave heights and periods of individual waves. The modification has overcome an inherent drawback of these joint PDFs that the mean wave period is infinite. A comparison is made between the modified formulae and the field data of Goda, which shows that the new formulae consist with the measurement better than their original counterparts.

Joint Distribution of Wave Heights and Wavelengths and Distribution of Wave Steepness

A joint probability density is derived for wavelengths and wave heights. It is asymmetric and depends only on the spectral bandwidth epsilon defined by Cartwright and Longuet-Higgins (1956). After that a theoretical probability density for wave steepness is obtained. It tends to Rayleigh distribution as epsilon --> 0. A comparison between theoretical steepness distribution and laboratory experiment result shows good agreement.

Application of Maximum Entropy Principle to Studying the Distribution of Wave Heights in A Random Wave Field

Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.

The seasonal variations in the significant wave height and sea surface wind speed of the China's seas

Long-term variations in a sea surface wind speed （WS） and a significant wave height （SWH） are associated with the global climate change, the prevention and mitigation of natural disasters, and an ocean resource exploitation, and other activities. The seasonal characteristics of the long-term trends in China＇s seas WS and SWH are determined based on 24 a （1988-2011） cross-calibrated, multi-platform （CCMP） wind data and 24 a hindcast wave data obtained with the WAVEWATCH-III （WW3） wave model forced by CCMP wind data. The results show the following. （1） For the past 24 a, the China＇s WS and SWH exhibit a significant increasing trend as a whole, of 3.38 cm/（s.a） in the WS, 1.3 cm/a in the SWH. （2） As a whole, the increasing trend of the China＇s seas WS and SWH is strongest in March-April-May （MAM） and December-January-February （DJF）, followed by June-July-August （JJA）, and smallest in September-October-November （SON）. （3） The areal extent of significant increases in the WS was largest in MAM, while the area decreased in JJA and DJF; the smallest area was apparent in SON. In contrast to the WS, almost all of China＇s seas exhibited a significant increase in SWH in MAM and DJF; the range was slightly smaller in JJA and SON. The WS and SWH in the Bohai Sea, the Yellow Sea, East China Sea, the Tsushima Strait, the Taiwan Strait, the northern South China Sea, the Beibu Gull and the Gulf of Thailand exhibited a significant increase in all seasons. （4） The variations in China＇s seas SWH and WS depended on the season. The areas with a strong increase usually appeared in DJF.

Estimation of Extreme Coastal Wave Heightsfrom Time Series of Wave Data

A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Australia, is analyzed to generate a set of storm peak wave heights by use of the Peaks-Over-Threshold method. The probability distribution is calculated by grouping the observod storm peak wave heights into a number of wave height classes and assigning a probability to each wave height class. The observed probability distribution is then fitted to eight different probability distribution functions and found to be fitted best by the Weibull distribution （a = 1.17）, nearly best by the FT-Ⅰ, quite well by the exponential, and poorly by the lognormal function based on the criterion of the sum of squares of the errors, SSE （H）. The effect of the threshold wave height on the estimated extreme wave height is also studied and is found insignificant in this study. The 95 % prediction intervals of the best-fit FT-Ⅰ , exponential and Weibull functions are also derived.

A forecasting model for wave heights based on a long short-term memory neural network

To explore new operational forecasting methods of waves,a forecasting model for wave heights at three stations in the Bohai Sea has been developed.This model is based on long short-term memory(LSTM)neural network with sea surface wind and wave heights as training samples.The prediction performance of the model is evaluated,and the error analysis shows that when using the same set of numerically predicted sea surface wind as input,the prediction error produced by the proposed LSTM model at Sta.N01 is 20%,18%and 23%lower than the conventional numerical wave models in terms of the total root mean square error(RMSE),scatter index(SI)and mean absolute error(MAE),respectively.Particularly,for significant wave height in the range of 3–5 m,the prediction accuracy of the LSTM model is improved the most remarkably,with RMSE,SI and MAE all decreasing by 24%.It is also evident that the numbers of hidden neurons,the numbers of buoys used and the time length of training samples all have impact on the prediction accuracy.However,the prediction does not necessary improve with the increase of number of hidden neurons or number of buoys used.The experiment trained by data with the longest time length is found to perform the best overall compared to other experiments with a shorter time length for training.Overall,long short-term memory neural network was proved to be a very promising method for future development and applications in wave forecasting.

Revisiting the seasonal wave height variability in the South China Sea with merged satellite altimetry observations

The seasonal variability of the significant wave height（SWH） in the South China Sea（SCS） is investigated using the most up-to-date gridded daily altimeter data for the period of September 2009 to August 2015. The results indicate that the SWH shows a uniform seasonal variation in the whole SCS, with its maxima occurring in December/January and minima in May. Throughout the year, the SWH in the SCS is the largest around Luzon Strait（LS） and then gradually decreases southward across the basin. The surface wind speed has a similar seasonal variation, but with different spatial distributions in most months of the year. Further analysis indicates that the observed SWH variations are dominated by swell. The wind sea height, however, is much smaller. It is the the largest in two regions southwest of Taiwan Island and southeast of Vietnam Coast during the northeasterly monsoon, while the largest in the central/southern SCS during the southwesterly monsoon. The extreme wave condition also experiences a significant seasonal variation. In most regions of the northern and central SCS, the maxima of the 99 th percentile SWH that are larger than the SWH theoretically calculated with the wind speed for the fully developed seas mainly appear in August–November, closely related to strong tropical cyclone activities.Compared with previous studies, it is also implied that the wave climate in the Pacific Ocean plays an important role in the wave climate variations in the SCS.

A New Method for Determining Threshold in Using PGCEVD to Calculate Return Values of Typhoon Wave Height

In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution （P-III） model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-III model and can be used for the return wave height in every direction.

Joint Occurrence Period of Wind Speed and Wave Height Based on Both Service Term and Risk Probability

Return periods calculated for different environmental conditions are key parameters for ocean platform design.Many codes for offshore structure design give no consideration about the correlativity among multi-loads and over-estimate design values.This frequently leads to not only higher investment but also distortion of structural reliability analysis.The definition of design return period in existing codes and industry criteria in China are summarized.Then joint return periods of different ocean environmental parameters are determined from the view of service term and danger risk.Based on a bivariate equivalent maximum entropy distribution,joint design parameters are estimated for the concomitant wave height and wind speed at a site in the Bohai Sea.The calculated results show that even if the return period of each environmental factor,such as wave height or wind speed,is small,their combinations can lead to larger joint return periods.Proper design criteria for joint return period associated with concomitant environmental conditions will reduce structural size and lead to lower investment of ocean platforms for the exploitation of marginal oil field.

A new method to estimate wave height of specified return period

In this paper, we propose a new method to estimate the wave height of a specifi c return period based on the Hurst rule and a self-affi ne fractal formula. A detailed description of our proposed model is presented in this paper. We use the proposed model to analyze wave height data recorded along the coast of Chaolian Island from 1963 to 1989. The results show that the performance of our proposed model in estimating design wave heights is superior to traditional models.

A Maximum-Entropy Compound Distribution Model for Extreme Wave Heights of Typhoon-Affected Sea Areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.