Study of the ability of SWOT to detect sea surface height changes caused by internal solitary waves

Surface Water and Ocean Topography(SWOT)is a next-generation radar altimeter that offers high resolution,wide swath,imaging capabilities.It has provided free public data worldwide since December 2023.This paper aims to preliminarily analyze the detection capabilities of the Ka-band radar interferometer(KaRIn)and Nadir altimeter(NALT),which are carried out by SWOT for internal solitary waves(ISWs),and to gather other remote sensing images to validate SWOT observations.KaRIn effectively detects ISW surface features and generates surface height variation maps reflecting the modulations induced by ISWs.However,its swath width does not completely cover the entire wave packet,and the resolution of L2/L3 level products(about 2 km)cannot be used to identify ISWs with smaller wavelengths.Additionally,significant wave height(SWH)images exhibit blocky structures that are not suitable for ISW studies;sea surface height anomaly(SSHA)images display systematic leftright banding.We optimize this imbalance using detrending methods;however,more precise treatment should commence with L1-level data.Quantitative analysis based on L3-level SSHA data indicates that the average SSHA variation induced by ISWs ranges from 10 cm to 20 cm.NALTs disturbed by ISWs record unusually elevated SWH and SSHA values,rendering the data unsuitable for analysis and necessitating targeted corrections in future retracking algorithms.For the normalized radar cross section,Ku-band and four-parameter maximum likelihood estimation retracking demonstrated greater sensitivity to minor changes in the sea surface,making them more suitable for ISW detection.In conclusion,SWOT demonstrates outstanding capabilities in ISW detection,significantly advancing research on the modulation of the sea surface by ISWs and remote sensing imaging mechanisms.

WavewatchⅢ模拟和统计方法在最大波高预报方面的评测分析

为了研究WavewatchⅢ(WWⅢ)海浪模型对最大波高的模拟能力及其与传统统计关系方法的差异,通过对两次台风浪过程的后报模拟和半年的业务化预报,分析了WWⅢ数值模拟的准确度及其与统计关系方法的精度差异。研究结果表明:WWⅢ数值模拟的最大波高(Hmax)的精度略低于有效波高(Hs),但也达到了24 h预报相对误差(H_(max)≥1 m)低于18%、相关系数高于0.94的水平,模拟精度可靠,可以用于业务化预报;与两种统计关系方法(H_(max)和H_(s)分别为1.42和1.52)计算的最大波高相比,数值模拟的精度总体与其相当,但在H_(max)和H_(s)比值大于1.65这种易出现危险的海况下,数值模拟具有更高的准确性,更适合应用于海浪预警报服务。

Joint Return Value Estimation of Significant Wave Heights and Wind Speeds with Bivariate Copulas

The joint design criteria of significant wave heights and wind speeds are quite important for the structural reliability of fixed offshore platforms.However,the design method that regards different ocean environmental variables as independent is conservative.In the present study,we introduce a bivariate sample consisting of the maximum wave heights and concomitant wind speeds of the threshold by using the peak-over-threshold and declustering methods.After selecting the appropriate bivariate copulas and univariate distributions and blocking the sample into years,the bivariate compound distribution of annual extreme wave heights and concomitant wind speeds is constructed.Two joint design criteria,namely,the joint probability density method and the conditional probability method,are applied to obtain the joint return values of significant wave heights and wind speeds.Results show that(28.5±0.5)m s^(-1)is the frequently obtained wind speed based on the Atlantic dataset,and these joint design values are more appropriate than those calculated by univariate analysis in the fatigue design.

Significant wave height forecasts integrating ensemble empirical mode decomposition with sequence-to-sequence model

As wave height is an important parameter in marine climate measurement,its accurate prediction is crucial in ocean engineering.It also plays an important role in marine disaster early warning and ship design,etc.However,challenges in the large demand for computing resources and the improvement of accuracy are currently encountered.To resolve the above mentioned problems,sequence-to-sequence deep learning model(Seq-to-Seq)is applied to intelligently explore the internal law between the continuous wave height data output by the model,so as to realize fast and accurate predictions on wave height data.Simultaneously,ensemble empirical mode decomposition(EEMD)is adopted to reduce the non-stationarity of wave height data and solve the problem of modal aliasing caused by empirical mode decomposition(EMD),and then improves the prediction accuracy.A significant wave height forecast method integrating EEMD with the Seq-to-Seq model(EEMD-Seq-to-Seq)is proposed in this paper,and the prediction models under different time spans are established.Compared with the long short-term memory model,the novel method demonstrates increased continuity for long-term prediction and reduces prediction errors.The experiments of wave height prediction on four buoys show that the EEMD-Seq-to-Seq algorithm effectively improves the prediction accuracy in short-term(3-h,6-h,12-h and 24-h forecast horizon)and long-term(48-h and 72-h forecast horizon)predictions.

Long-Term Extreme Wave Characteristics in the Water Adjacent to China Based on ERA5 Reanalysis Data

Extreme waves have a profound impact on coastal infrastructure;thus,understanding the variation law of risky analysis and disaster prevention in coastal zones is necessary.This paper analyzed the spatiotemporal characteristics of extreme wave heights adjacent to China from 1979 to 2018 based on the ERA5 datasets.Nonstationary extreme value analysis is undertaken in eight repre-sentative points to investigate the trends in the values of 50-and 100-year wave heights.Results show that the mean value of extreme waves is the largest in the eastern part of Taiwan Island and the smallest in the Bohai Sea from 1979 to 2018.Only the extreme wave height in the northeastern part of Taiwan Island shows a significant increase trend in the study area.Nonstationary analysis shows remarkable variations in the values of 50-and 100-year significant wave heights in eight points.Considering the annual mean change,E1,E2,S1,and S2 present an increasing trend,while S3 shows a decreasing trend.Most points for the seasonal mean change demon-strate an increasing trend in spring and winter,while other points show a decreasing trend in summer and autumn.Notably,the E1 point growth rate is large in autumn,which is related to the change in typhoon intensity and the northward movement of the typhoon path.

Estimation of peak wave period from surface texture motion in videos

Wave information retrieval from videos captured by a single camera has been increasingly applied in marine observation.However,when the camera observes ocean waves at low grazing angles,the accurate extraction of wave information from videos will be affected by the interference of the fine ripples on the sea surface.To solve this problem,this study develops a method for estimating peak wave periods from videos captured at low grazing angles.The method extracts the motion of the sea surface texture from the video and obtains the peak wave period via the spectral analysis.The calculation results captured from real-world videos are compared with those obtained from X-band radar inversion and tracking buoy movement,with maximum deviations of 8%and 14%,respectively.The analysis of the results shows that the peak wave period of the method has good stability.In addition,this paper uses a pinhole camera model to convert the displacement of the texture from pixel height to actual height and performs moving average filtering on the displacement of the texture,thus conducting a preliminary exploration of the inversion of significant wave height.This study helps to extend the application of sea surface videos.

Long-Term Characterization of Sea Conditions in the East China Sea Using Significant Wave Height and Wind Speed

In this study, the statistical characterization of sea conditions in the East China Sea(ECS) is investigated by analyzing a significant wave height and wind speed data at a 6-hour interval for 30 years(1980–2009), which was simulated and computed using the WAVEWATCH Ⅲ(WW3) model. The monthly variations of these parameters showed that the significant wave height and wind speed have minimum values of 0.73 m and 5.15 ms^(-1) and 1.73 m and 8.24 ms^(-1) in the month of May and December, respectively. The annual, seasonal, and monthly mean sea state characterizations showed that the slight sea generally prevailed in the ECS and had nearly the highest occurrence in all seasons and months. Additionally, the moderate sea prevailed in the winter months of December and January, while the smooth(wavelets) sea prevailed in May. Furthermore, the spatial variation of sea states showed that the calm and smooth sea had the largest occurrences in the northern ECS. The slight sea occurred mostly(above 30%) in parts of the ECS and the surrounding locations, while higher occurrences of the rough and very rough seas were distributed in waters between the southwest ECS and the northeast South China Sea(SCS). The occurrences of the phenomenal sea conditions are insignificant and are distributed in the northwest Pacific and its upper region, which includes the Southern Kyushu-Palau Ridge and Ryukyu Trench.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Wave height statistical characteristic analysis

When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year observation data to derive 100-year return period design wave height. Therefore, the study of inherent self-similarity in ocean hydrological elements becomes increasingly important to the study of multi-year return period design wave height derivation. In this paper, we introduced multifractal to analyze the statistical characteristics of wave height series data observed from oceanic hydrological station. An improvement is made to address the existing problems of the multifractal detrended fluctuation analysis (MF-DFA) method, where trend function showed a discontinuity between intervals. The improved MFDFA method is based on signal mode decomposition, replacing piecewise polynomial fitting used in the original method. We applied the proposed method to the wave height data collected at Chaolian Island, Shandong, China, from 1963 to 1989 and was able to conclude the wave height sequence presented weak multi-fractality. This result provided strong support to the past research on the derivation of multi-year return period design wave height with observed data. Moreover, the new method proposed in this paper also provides a new perspective to explore the intrinsic characteristic of data.

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.

Numerical Study of the Impact of Climate Change on Irregular Wave Run-up Over Reef-Fringed Coasts

Wave hydrodynamics over fringing reefs is largely controlled by the reef surface roughness and hydrodynamic forcing.It is believed that climate change will result in a net increase in the water depth over the reef flat,a degrading of the surface roughness of coral reefs and changes in extreme incident wave heights.For an accurate assessment of how climate change affects the safety of reef-fringed coasts,a numerical study of the impact of climate change on irregular wave run-up over reef-fringed coasts was carried out based on a Boussinesq wave model,FUNWAVE-TVD.Validated with experimental data,the present model shows reasonable prediction of irregular wave evolution and run-up height over fringing reefs.Numerical experiments were then implemented based on the anticipated effects of climate change and carried out to investigate the effects of sea level rise,degrading of the reef surface roughness and increase of extreme incident wave height on the irregular wave run-up height over the backreef beach respectively.Variations of run-up components(i.e.,spectral characteristics of run-up and mean water level)were examined specifically and discussed to better understand the influencing mechanism of each climate change-related effect on the run-up.