Metocean design parameter estimation for fixed platform based on copula functions

Considering the dependent relationship among wave height, wind speed, and current velocity, we construct novel trivariate joint probability distributions via Archimedean copula functions. Total 30-year data of wave height, wind speed, and current velocity in the Bohai Sea are hindcast and sampled for case study. Four kinds of distributions, namely, Gumbel distribution, lognormal distribution, Weibull distribution, and Pearson Type III distribution, are candidate models for marginal distributions of wave height, wind speed, and current velocity. The Pearson Type III distribution is selected as the optimal model. Bivariate and trivariate probability distributions of these environmental conditions are established based on four bivariate and trivariate Archimedean copulas, namely, Clayton, Frank, Gumbel-Hougaard, and Ali-Mikhail-Haq copulas. These joint probability models can maximize marginal information and the dependence among the three variables. The design return values of these three variables can be obtained by three methods: univariate probability, conditional probability, and joint probability. The joint return periods of different load combinations are estimated by the proposed models. Platform responses (including base shear, overturning moment, and deck displacement) are further calculated. For the same return period, the design values of wave height, wind speed, and current velocity obtained by the conditional and joint probability models are much smaller than those by univariate probability. Considering the dependence among variables, the multivariate probability distributions provide close design parameters to actual sea state for ocean platform design.     

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 preliminary study on the intensity of cold wave storm surges of Laizhou Bay

Dike failure and marine losses are quite prominent in Laizhou Bay during the period of cold wave storm surges because of its open coastline to the north and flat topography. In order to evaluate the intensity of cold wave storm surge, the hindcast of marine elements induced by cold waves in Laizhou Bay from 1985 to 2004 is conducted using a cold wave storm surge–wave coupled model and the joint return period of extreme water level, concomitant wave height, and concomitant wind speed are calculated. A new criterion of cold wave storm surge intensity based on such studies is developed. Considering the frequency of cold wave, this paper introduces a Poisson trivariate compound reconstruction model to calculate the joint return period, which is closer to the reality. By using the newly defined cold wave storm surge intensity, the ‘cold wave grade' in meteorology can better describe the severity of cold wave storm surges and the warning level is well corresponding to different intensities of cold wave storm surges. Therefore, it provides a proper guidance to marine hydrological analysis, disaster prevention and marine structure design in Laizhou Bay.     

Long-term variation of storm surge-associated waves in the Bohai Sea

When investigating the long-term variation of wave characteristics as associated with storm surges in the Bohai Sea, the Simulating Waves Nearshore(SWAN) model and ADvanced CIRCulation(ADCIRC) model were coupled to simulate 32 storm surges between 1985 and 2014. This simulation was validated by reproducing three actual wave processes, showing that the simulated significant wave height(SWH) and mean wave period agreed well with the actual measurements. In addition, the long-term variations in SWH, patterns in SWH extremes along the Bohai Sea coast, the 100-year return period SWH extreme distribution, and waves conditional probability distribution were calculated and analyzed. We find that the trend of SWH extremes in most of the coastal stations was negative, among which the largest trend was-0.03 m/a in the western part of Liaodong Bay. From the 100-year return period of the SWH distribution calculated in the Gumbel method, we find that the SWH extremes associated with storm surges decreased gradually from the center of the Bohai Sea to the coast. In addition, the joint probability of wave and surge for the entire Bohai Sea in 100-year return period was determined by the Gumbel logistic method. We therefore, assuming a minimum surge of one meter across the entire Bohai Sea, obtained the spatial SWH distribution. The conclusions of this study are significant for offshore and coastal engineering design.     

Evaluating the Accuracy of ERA5 Wave Reanalysis in the Water Around China

Wave parameters, such as wave height and wave period, are important for human activities, such as navigation, ocean engineering and sediment transport, etc. In this study, wave data from six buoys around Chinese waters, are used to assess the quality of wave height and wave period in the ERA5 reanalysis of the European Centre for Medium-Range Weather Forecasts. Annual hourly data with temporal resolution are used. The difference between the significant wave height(SWH) of ERA 5 and that of the buoy varies from-0.35 m to 0.30 m for the three shallow locations;for the three deep locations, the variation ranges from-0.09 m to 0.09 m. The ERA5 SWH data show positive biases, indicating an overall overestimation for all locations, except for E2 and S1 where underestimation is observed. During the tropical cyclone period, a large(about 32%) underestimation of the maximum SWH in the ERA5 data is observed. Hence, the ERA5 SWH data cannot be used for design applications without site-specific validation. The difference between the annual wave period from ERA5 and the mean wave period from the buoys varies from-1.31 s to 0.4 s. Inter-comparisons suggest that the ERA5 dataset is consistent with the annual mean SWH. However, for the average period, the performance is not good, and half of the correlation coefficients in the four points are less 50%. Overall, the deep water area simulation effect is better than that in the shallow water.     

Stochastic Model for Estimating Extreme Water Level in Port and Coastal Engineering Design

Extreme water level is an important consideration when designing coastal protection structures. However, frequency analysis recommended by standard codes only considers the annual maximum water level, whereas water levels should actually be regarded as a combination of astronomical tide and storm surge. The two impacting factors are both random variables, and this paper discusses their dependency structures and proposes a new joint probability method to determine extreme design water levels. The lognormal, Gumbel, Weibull, Pearson type 3, traditional maximum entropy, and modified maximum entropy distributions are applied to fit univariate data of astronomical tides and storm surges separately, and the bivariate normal, Gumbel-Hougaard, Frank and Clayton copulas are then utilized to construct their joint probability distributions. To ensure that the new design method is suitable for use with typhoon data, the annual occurrence frequency of typhoon processes is considered and corresponding bivariate compound probability distributions are proposed. Based on maximum water level data obtained from Hengmen hydrological station in the Pearl River Basin, China, these probability models are applied to obtain designs for extreme water levels using the largest sum of the astronomical tide and storm surge obtained under fixed joint return periods. These design values provide an improved approach for determining the necessary height of coastal and offshore structures.     

Measurements of ocean wave and current field using dual polarized X-band radar

A new ocean wave and sea surface current monitoring system with horizontally-(HH) and vertically-(VV) polarized X-band radar was developed. Two experiments into the use of the radar system were carried out at two sites, respectively, for calibration process in Zhangzi Island of the Yellow Sea, and for validation in the Yellow Sea and South China Sea. Ocean wave parameters and sea surface current velocities were retrieved from the dual polarized radar image sequences based on an inverse method. The results obtained from dual-polarized radar data sets acquired in Zhangzi Island are compared with those from an ocean directional buoy. The results show that ocean wave parameters and sea surface current velocities retrieved from radar image sets are in a good agreement with those observed by the buoy. In particular, it has been found that the vertically-polarized radar is better than the horizontally-polarized radar in retrieving ocean wave parameters, especially in detecting the significant wave height below 1.0 m.     

A New Multigrid 3D-VAR Optimization Method for Bottom Friction Using HF Radar Current Observation

This paper proposes a new method for data assimilation of the surface radial current observed by High Frequency ground wave radar and optimization of the bottom friction coefficient. In this method, the shallow water wave equation is introduced into the cost function of the multigrid three-dimensional variation data assimilation method as the weak constraint term, the surface current and the bottom friction coefficient are defined as the analytical variables, and the high spatiotemporal resolution surface radial flow observed by the high-frequency ground wave radar is used to optimize the surface current and bottom friction coefficient. This method can effectively consider the spatiotemporal correlation of radar data and extract multiscale information from surface radial flow data from long waves to short waves. Introducing the shallow water wave equation into the cost function as a weak constraint condition can adjust both the momentum and mass fields simultaneously to obtain more reasonable analysis information. The optimized bottom friction coefficient is introduced into the regional ocean numerical model to carry out numerical experiments. The test results show that the bottom friction coefficient obtained by this method can effectively improve the accuracy of the numerical simulation of sea surface height in the offshore area and reduce the simulation error.     

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.     

Analysis of Dynamic Characteristics of the 21st Century Maritime Silk Road

The 21st century Maritime Silk Road(MSR) proposed by China strongly promotes the maritime industry. In this paper, we use wind and ocean wave datasets from 1979 to 2014 to analyze the spatial and temporal distributions of the wind speed, significant wave height(SWH), mean wave direction(MWD), and mean wave period(MWP) in the MSR. The analysis results indicate that the Luzon Strait and Gulf of Aden have the most obvious seasonal variations and that the central Indian Ocean is relatively stable. We analyzed the distributions of the maximum wind speed and SWH in the MSR over this 36-year period. The results show that the distribution of the monthly average frequency for SWH exceeds 4 m(huge waves) and that of the corresponding wind speed exceeds 13.9 ms~(-1)(high wind speed). The occurrence frequencies of huge waves and high winds in regions east of the Gulf of Aden are as high as 56% and 80%, respectively. We also assessed the wave and wind energies in different seasons. Based on our analyses, we propose a risk factor(RF) for determining navigation safety levels, based on the wind speed and SWH. We determine the spatial and temporal RF distributions for different seasons and analyze the corresponding impact on four major sea routes. Finally, we determine the spatial distribution of tropical cyclones from 2000 to 2015 and analyze the corresponding impact on the four sea routes. The analysis of the dynamic characteristics of the MSR provides references for ship navigation as well as ocean engineering.     

Comparison of TOPEX/POSEIDON altimeter derived wave period with ocean buoy data in the East China Sea and South China Sea

Altimeter wave period data obtained from continental shelf seas are analyzed in this paper. Empirical models are introduced for zero up-crossing and peak wave period calculation with TOPEX/POSEIDON data. Their performances are assessed using independent validation dataset in four sites in the open ocean of China. To provide more accurate wave period estimation, new coefficients are applied to reliable in situ data. Comparison of our estimated the wave periods with new linear calibrations based on independent data of Seapac 2100 deployed in the East China Sea and South China Sea showed that the accuracy was improved over estimates determined from earlier empirical models. Regional analysis indicated that the wave period model works better under wind sea condition.     

The development of a new real-time subsurface mooring

Subsurface mooring allows researchers to measure the ocean properties suchas water te mperature,salinity,and velocity at several depths of the water column for a long period.Traditional subsurface mooring can release data only after recovered,which constrains the usage of the subsurface and deep layer data in the ocean and climate predictions.Recently,we developed a new real-time subsurface mooring(RTSM).Velocity profiles over upper 1 000 m depth and layered data from sensors up to 5 000 m depth can be realtime transmitted to the small surface buoy through underwater acoustic communication and then to the office through Beidou or Iridium satellite.To verify and refine their design and data transmission process,we deployed more than 30 sets of RTSMs in the western Pacific to do a 1-year continuous run during2016-2018.The continuous running period of RTSM in a 1-year cycle can reach more than 260 days on average,and more than 95% of observed data can be successfully transmitted back to the office.Compared to the widely-used inductive coupling communication,wireless acoustic communication has been shown more applicable to the underwater sensor network with large depth intervals and long transmission distance to the surface.     

The fractional power law of wind wave growth in deep water for short fetch

Combining the 3/2 power law proposed by Toba with the significant wave energy balance equation for wind waves, wave growth in deep water for short fetch is investigated. It is found that the variations of wave height and period with fetch have the form of power function with fractional exponents 3/8 and 1/4 respectively. Using these exponents in the power functions and through data fitting, the concise wind wave growth relations for short fetch are obtained.     

Parameterized first-guess spectrum method for retrieving directional spectrum of swell-dominated waves and huge waves from SAR images

A method to retrieve ocean wave spectra from SAR images, named Parameterized First-guess Spectrum Method (PFSM), was proposed after interpretation of the theory to ocean wave imaging and analysis of the drawbacks of the retrieving model generally used. In this method, with additional information and satellite parameters, the separating wave-number is first calculated to determine the maximum wave-number beyond which the linear relation can be used. The separating wave-number can be calculated using the additional information on wind velocity and parameters of SAR satellite. And then the SAR spectrum can be divided into SAR spectrum of wind wave and of swell according to the result of separating wave-number. The portion of SAR spectrum generated by wind wave, is used to search for the most suitable parameters of ocean wind wave spectrum, including propagation direction of ocean wave, phase speed of dominating wave and the angle spreading coefficient. The swell spectrum is acquired by directly inversing the linear relation of ocean wave spectrum to SAR spectrum given the portion of SAR spectrum generated by swell. We used the proposed method to retrieve the ocean wave spectrum from ERS-SAR data from the South China Sea and compared the result with altimeter data. The agreement indicates that the PFSM is reliable.     

Elimination of the impact of vessels on ocean wave height inversion with X-band wave monitoring radar

Directional wave spectra and integrated wave parameters can be derived from X-band radar sea surface images.A vessel on the sea surface has a significant influence on wave parameter inversions that can be seen as intensive backscatter speckles in X-band wave monitoring radar sea surface images.A novel algorithm to eliminate the interference of vessels in ocean wave height inversions from X-band wave monitoring radar is proposed.This algorithm is based on the characteristics of the interference.The principal components(PCs) of a sea surface image sequence are extracted using empirical orthogonal function(EOF)analysis.The standard deviation of the PCs is then used to identify vessel interference within the image sequence.To mitigate the interference,a suppression method based on a frequency domain geometric model is applied.The algorithm framework has been applied to OSMAR-X,a wave monitoring system developed by Wuhan University,based on nautical X-band radar.Several sea surface images captured on vessels by OSMAR-X are processed using the method proposed in this paper.Inversion schemes are validated by comparisons with data from in situ wave buoys.The root-mean-square error between the significant wave heights(SWH) retrieved from original interference radar images and those measured by the buoy is reduced by 0.25 m.The determinations of surface gravity wave parameters,in particular SWH,confirm the applicability of the proposed method.     

Crest-height distribution of nonlinear random waves

The wave crest is an important factor for the design of both fixed and floating marine structures. Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damage. Many empirical and theoretical distribution functions for wave crest heights have been proposed, but there is a lack of agreement between them. It is of significance to develop a better new nonlinear wave crest height distribution model. The progress in the research of wave crest heights is reviewed in this paper. Based on Stokes’ wave theory, an approximate nonlinear wave crest-height distribution formula with simple parameters is derived. Two sets of measured data are presented and compared with various theoretical distributions of wave crests obtained from nonlinear wave models and analysis of the comparison is given in detail. The new crest-height distribution model agrees well with observations. Also, the new theoretical distribution is more accurate than the other methods cited in this paper and has a greater range of applications.     

Wave Height Estimation from SAR Imagery

This paper presents a method developed for estimating wave height from synthetic aperture radar (SAR) imagery without prior assumption of noise distribution. It is based on two-dimenslonal ocean wave spectra retrieved from fully calibrated SAR images. Wen‘s spectrum was used as first-guess wave spectrum in the retrieval process. Comparison of the estimated wave height obtained by this method from two ERS-1 SAR subimages dated 23 July 1994 with in-situ measurements showed that the method works well.     

A simple method to extract glacier length based on Digital Elevation Model and glacier boundaries for simple basin type glacier

Glacier length is a key morphological element that has many glaciological applications; however, it is often difficult to determine, especially for glaciers that cover larger spatial areas or those that exhibit frequent temporal change. In this paper, we describe a new ArcGIS-based method that can derive glacier flow lines for determining glacier length based on digital elevation model and glacier outlines. This method involves (1) extraction of the highest and lowest points on a glacier, (2) calculation of 10-m contour lines on the glacier from 10 m to 100 m height, and (3) connection of the midpoints of each contour line with the highest and the lowest points in order to create a flow line, which is subsequently smoothed. In order to assess the reliability of this method, we tested the algorithm’s results against flow lines calculated using field measurements, analysing data from the Chinese Glacier Inventory, and manual interpretation. These data showed that the new automated method is effective in deriving glacier flow lines when contour lines are relatively large; in particular, when they are between 70 m and 100 m. Nonetheless, a key limitation of the algorithm is the requirement to automatically delete repeated and closed curves in the pre-treatment processes. In addition to calculating glacier flow lines for derivation of glacier length, this method also can be used to effectively determine glacier terminus change.     

A Spatiotemporal Interactive Processing Bias Correction Method for Operational Ocean Wave Forecasts

Numerical models and correct predictions are important for marine forecasting,but the forecasting results are often unable to satisfy the requirements of operational wave forecasting.Because bias between the predictions of numerical models and the actual sea state has been observed,predictions can only be released after correction by forecasters.This paper proposes a spati-otemporal interactive processing bias correction method to correct numerical prediction fields applied to the production and release of operational ocean wave forecasting products.The proposed method combines the advantages of numerical models and Forecast Discussion;specifically,it integrates subjective and objective information to achieve interactive spatiotemporal correc-tions for numerical prediction.The method corrects the single-time numerical prediction field in space by spatial interpolation and sub-zone numerical analyses using numerical model grid data in combination with real-time observations and the artificial judg-ment of forecasters to achieve numerical prediction accuracy.The difference between the original numerical prediction field and the spatial correction field is interpolated to an adjacent time series by successive correction analysis,thereby achieving highly efficient correction for multi-time forecasting fields.In this paper,the significant wave height forecasts from the European Centre for Medium-Range Weather Forecasts are used as background field for forecasting correction and analysis.Results indicate that the proposed method has good application potential for the bias correction of numerical predictions under different sea states.The method takes into account spatial correlations for the numerical prediction field and the time series development of the numerical model to correct numerical predictions efficiently.