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.

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.

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 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.

Comparative analysis of significant wave height between a new Southern Ocean buoy and satellite altimeter

In-situ observation is restricted by the strong wind and waves in the Southern Ocean.A Westerlies EnvironmentalMonitoring Buoy(WEMB)was firstly deployed in the Southern Ocean during China’s 35th Antarctic Expedition,facilitating further understanding of the oceanic environmental characteristics of this region.With the develop-ment of technology and the improvement of data processing methods,the accuracy of satellite altimeter productsis constantly improved,thus making it possible to inspect and evaluate the in-situ observation data.Based on theL3 products of multiple satellite altimeters,this paper analyzes and corrects the significant wave height(SWH)data of WEMB by means of data matching,error statistics,and linear least-squares fitting.Through this study,the authors obtained the following results.The effect of gravitational acceleration changes with latitude on SWHaccuracy is fairly small.Due to the low response of WEMB to high-frequency waves,there is a systematic devia-tion.A feasible correction method is therefore proposed to improve the SWH accuracy of WEMB.The temporalvariation of the corrected SWH is highly consistent with that of the 10 m wind during the observation period,and its average value reaches 3.8 m.

Validation of significant wave height retrieval from co-polarization Chinese Gaofen-3 SAR imagery using an improved algorithm

Chinese Gaofen-3（GF-3） is the first civilian satellite to carry C-band（5.3 GHz） synthetic aperture radar（SAR）.During the period of August 2016 to December 2017, 1 523 GF-3 SAR images acquired in quad-polarization（vertical-vertical（VV）, horizontal-horizontal（HH）, vertical-horizontal（VH）, and horizontal-vertical（HV）） mode were recorded, mostly around China＇s seas. In our previous study, the root mean square error（RMSE） of significant wave height（SWH） was found to be around 0.58 m when compared with retrieval results from a few GF-3 SAR images in co-polarization（VV and HH） with moored measurements by using an empirical algorithm CSARWAVE. We collected a number of sub-scenes from these 1 523 images in the co-polarization channel,which were collocated with wind and SWH data from the European Centre for Medium-Range Weather Forecasts（ECMWF） reanalysis field at a 0.125° grid. Through the collected dataset, an improved empirical wave retrieval algorithm for GF-3 SAR in co-polarization was tuned, herein denoted as CSARWAVE2. An additional 92 GF-3 SAR images were implemented in order to validate CSARWAVE2 against SWH from altimeter Jason-2, showing an about 0.52 m RMSE of SWH for co-polarization GF-3 SAR. Therefore, we conclude that the proposed empirical algorithm has a good performance for wave retrieval from GF-3 SAR images in co-polarization.

Calculation of Significant Wave Height Using the Linear Mean Square Estimation Method

Significant wave height is an important criterion in designing coastal and offshore structures.Based on the orthogonality principle, the linear mean square estimation method is applied to calculate significant wave height in this paper.Twenty-eight-year time series of wave data collected from three ocean buoys near San Francisco along the California coast are analyzed.It is proved theoretically that the computation error will be reduced by using as many measured data as possible for the calculation of significant wave height.Measured significant wave height at one buoy location is compared with the calculated value based on the data from two other adjacent buoys.The results indicate that the linear mean square estimation method can be well applied to the calculation and prediction of significant wave height in coastal regions.

Significant wave height estimation using azimuth cutoff of C-band RADARSAT-2 single-polarization SAR images

This paper proposes two simple models, look-up table（LUT） model and empirical model, to directly retrieve significant wave height（Hs） using synthetic aperture radar（SAR） azimuth cutoff（λc）. Both models aim at C-band VV, HH, VH, and HV single-polarization SAR images. The LUT model relates Hs to λc, while the empirical model relates Hs to both λc and SAR range-to-velocity（β）. The LUT model coefficients are derived by simulation under different sea states and observation conditions, which depend on incidence angle（θ）, wave direction（dw）, and βbut are independent of polarization. The empirical model coefficients are obtained by fitting the collocated data,which only depend on polarization. To fit empirical model coefficients and validate the two models, C-band RADARSAT-2 fine quad-polarization（VV＋HH＋VH＋HV） single-look complex（SLC） SAR images and collocated buoy data are collected. Retrieved Hs, using Yang model and the two models proposed in this paper from four kinds of polarization SAR data, are compared with buoy Hs. Results show that both LUT and empirical models have the capacity of retrieving Hs from C-band RADARSAT-2 co-polarization SAR data, while Yang model is not suitable for these kinds of SAR data. Moreover, the empirical model is also valid for cross-polarization SAR data showing clear ocean wave stripes.

A new model to estimate significant wave heights with ERS-1/2 scatterometer data

A new model is proposed to estimate the significant wave heights with ERS-1/2 scatterometer data. The results show that the relationship between wave parameters and radar backscattering cross section is similar to that between wind and the radar backscattering cross section. Therefore, the relationship between significant wave height and the radar backscattering cross section is established with a neural network algorithm, which is, if the average wave period is ≤7s, the root mean square of significant wave height retrieved from ERS-1/2 data is 0.51 m, or 0.72 m if it is >7s otherwise.

Decadal Variability of Global Ocean Significant Wave Height

This paper presents the long-term climate changes of significant wave height(Hs) in 1958–2001 over the entire global ocean using the 45-year European Centre for Medium-Range Weather Forecasts(ECMWF) Reanalysis(ERA-40) wave data. The linear trends in Hs and regional and seasonal differences of the linear trends for Hs were calculated. Results show that the Hs exhibits a significant increasing trend of about 4.6 cm decade-1 in the global ocean as a whole over the last 44 years. The Hs changes slowly during the periods 1958–1974 and 1980–1991, while it increases consistently during the periods 1975–1980 and 1995–1998. The Hs reaches its lowest magnitude in 1975, with annual average wave height about 2 m. In 1992, the Hs has the maximum value of nearly 2.60 m. The Hs in most ocean waters has a significant increasing trend of 2–14 cm decade-1 over the last 44 years. The linear trend exhibits great regional differences. Areas with strong increasing trend of Hs are mainly distributed in the westerlies of the southern Hemisphere and the northern Hemisphere. Only some small areas show obvious decreasing in Hs. The long-term trend of Hs in DJF(December, January, February) and MAM(March, April, May) is much more stronger than that in JJA(June, July, August) and SON(September, October, November). The linear trends of the Hs in different areas are different in different seasons; for instance, the increasing trend of Hs in the westerlies of the Pacific Ocean mainly appears in MAM and DJF.

An evaluation of input/dissipation terms in WAVEWATCH Ⅲ using in situ and satellite significant wave height data in the South China Sea

A WAVEWATCH III version 3.14（WW3） wave model is used to evaluate input/dissipation source term packages WAM3, WAM4 and TC96 considering the effect of atmospheric instability. The comparisons of a significant wave height acquired from the model with different packages have been performed based on wave observation radar and HY-2 altimetry significant wave height data through five experiments in the South China Sea domain spanning latitudes of 0°–35°N and longitudes of 100°–135°E. The sensitivity of the wind speed correction parameter in the TC96 package also has been analyzed. From the results, the model is unable to dissipate the wave energy efficiently during a swell propagation with either source packages. It is found that TC96 formulation with the ＂effective wind speed＂ strategy performs better than WAM3 and WAM4 formulations. The wind speed correction parameter in the TC96 source package is very sensitive and needs to be calibrated and selected before the WW3 model can be applied to a specific region.

Calibration of HY-2A satellite significant wave heights with in situ observation

Significant wave height（SWH） can be computed from the returning waveform of radar altimeter, this parameter is only raw estimates if it does not calibrate. But accurate calibration is important for all applications, especially for climate studies. HY-2a altimeter has been operational since April 2012 and its products are available to the scientific community. In this work, SWH data from HY-2A altimeters are calibrated against in situ buoy data from the National Data Buoy Center（NDBC）, Distinguished from previous calibration studies which generally regarded buoy data as ＂truth＂, the work of calibration for HY-2A altimeter wave data against in situ buoys was applied a more sophisticated statistical technique-the total least squares（TLS） method which can take into account errors in both variables. We present calibration results for HY-2A radar altimeter measurement of wave height against NDBC buoys. In addition, cross-calibration for HY-2A and Jason-2 wave data are talked over and the result is given.

Shenzhou-4 spaceborne altimeter waveform processing and significant wave height retrieval

The Shenzhou -4 spaceborne （SZ -4） altimeter waveforms were processed, and then the significant wave heights （SWH） was retrieved on the basis of waveform fitting and waveform retracking. Waveforms processing includes the waveform ls averaging, the elimination of thermal noise and the waveforms normalization. Double peaks were found on each SZ - 4 waveform, and it was pointed out that the region of waveforms with the second peak is abnormal and its effects on the whole waveform in the waveform fit should be taken into consideration. To obtain the width of the waveform leading-edge, a method was proposed to find the starting point of waveform, and the half-power point of waveform was found by retracking the waveform. The normalized wavefornis were fitted with the Haynes model by using the weighting least square fit method. Then the selections of the weighting coefficients and their effects on significant wave hight retrieving were discussed, and the optimal five-region weighting method was proposed. At last, the SWH data of SZ -4 altimeter retrieved by using the proposed method were compared with those of ERS -2 and Jason - 1 altimeter, and it was concluded that the SZ -4 altimeter can detect significant wave height.

Quality evaluation and calibration of the SWIM significant wave height product with buoy data

The significant wave height(SWH)is one of the main parameters that describe wave characteristics and is widely used in wave research fields.Wave parameters measured by radar are influenced by the offshore distance and sea state.Validation and calibration are of great significance for radar data applications.The nadir beam of surface wave investigation and monitoring(SWIM)detects the global-ocean-surface SWH.To determine the product quality of SWIM SWH,this paper carried out time-space matching between SWIM and buoy data.The data qualities were evaluated under different offshore distances and sea states.An improved calibration method was proposed based on sea state segmentation,which considered the distribution of the point collocation numbers in various sea states.The results indicate that(1)the SWIM SWH accuracy at offshore distances greater than 50 km is higher than that at distances less than 50 km,with an root mean squared error(RMSE)of 0.2444 m,scatter index(SI)of 0.1156 and relative error(RE)of 9.97%at distances greater than 50 km and those of 0.4460 m,0.2230 and18.66%at distances less than 50 km.(2)SWIM SWH qualities are better in moderate and rough sea states with RMSEs of 0.2848 m and 0.3169 m but are worse in slight and very rough sea states.(3)The effect of the improved calibration method is superior to the traditional method in each sea state and overall data,and the RMSE of SWIM SWH is reduced from the raw 0.3135 m to 0.2859 m by the traditional method and 0.1982 m by the improved method.The influence of spatiotemporal window selection on data quality evaluation was analyzed in this paper.This paper provides references for SWIM SWH product applications.

Regional Frequency Analysis of Significant Wave Heights Based onL-moments

L-moments are defined as linear combinations of probability-weighted moments, They are, virtually unbiased for small samples, and perform well in parameter estimation, choice of the distribution type and regional analysis. The traditional methods of determining the design wave heights for planning marine structures use data only from the site of interest. Regional frequency analysis gives a new approach to estimate quantile by use of the homogeneous neighborhood informatian. A regional frequency analysis based on L-moments with a case study of the California coast is presented. The significant wave height data for the California coast is offered by NDBC. A 6-site region without 46023 is considered to be a homogeneous region, whose optimal regional distribution is Pearson Ⅲ. The test is conducted by a simulation process. The regional quantile is compared with the at-site quantile, and it is shown that efficient neighborhood information can be used via regional frequency analysis to give a reasonable estimation of the site without enough historical data.

Multi-scale wavelet analysis of TOPEX/Poseidon altimeter significant wave height in eastern China seas

The multi-scale characteristics of wave significant height （Hs） in eastern China seas were revealed by multi-scale wavelet analysis. In order to understand the relation between wave and wind, the TOPEX/Poseidon measurements of Hs and wind speed were analyzed. The result showed that Hs and wind speed change in multi-scale at one-, two-month, half-, one- and two-year cycles. But in a larger time scale, the variations in Hs and wind speed are different. Hs has a five-year cycle similar to the cycle of ENSO variation, while the wind speed has no such cycle. In the time domain, the correlation between Hs and ENSO is unclear.

Retrieval of Significant Wave Height Under Typhoon Conditions from Gaofen-3 SAR Imagery

The objective of this paper is to propose an empirical method to inverse significant wave height(SWH)under typhoon conditions from collected dual-polarization Gaofen(GF)-3 synthetic aperture radar(SAR)imagery.The typhoon scenes were cap-tured from narrow scan(NSC)and wide scan(WSC)images,and collocated with European Center for Medium-Range Weather Fore-casts reanalysis data of(ECMWF).To improve the quality of GF-3 SAR images,the recalibration over rainforest and de-scalloping were carried out.To establish the empirical relationship between SAR-derived parameters and collocated SWH,the sensitivity analysis of typical parameters about the normalized radar cross section(Nrcs)and imagery variance(Cvar)were performed to both VV and VH polarized images.Four scenes from GF-3 SAR imagery under typhoon conditions were used for training the model by the multivari-ate least square regression,and one scene was used for preliminary validation.It was found that the joint retrieval model based on VV and VH polarized SAR imagery performed better than any single polarized model.These results,verified by using ECMWF data,revealed the soundness of this approach,with a correlation of 0.95,bias of 0 m,RMSE of 0.44 and SI of 0.01 when VV polarization and VH polarization data were both used.

Significant wave height prediction through artificial intelligent mode decomposition for wave energy management

The prediction of significant wave height(SWH)is crucial for managing wave energy.While many machine learning studies have focused on accurately predicting SWH values within hours in advance,the primary concern should be given to the level of the wave height for real-world applications.In this paper,a classification framework for the time-series of SWH based on Transformer encoder(TF)and empirical mode decomposition(EMD)is developed,which can provide a lead time of 6 to 48 h with the fixed thresholds of 2 m for high level waves and 1.5 m for low level waves.The performance of this approach is compared to that of three mainstream algorithms with and without EMD features.Results from the datasets collected from buoy measurements in the Atlantic Ocean indicate that the optimal mean accuracy at a lead time of 6 h was 99.1%and the average training time was 75 s,demonstrating the accuracy and efficiency of this proposed model.This study provides valuable tools and references for real-world SWH prediction applications.