由模拟波面分析双峰谱型海浪的统计特征

采用目前国际上最新的随机波分析方法,由协方差矩阵的循环嵌套技术,对美国国家浮标44008站2002年6月一典型的双峰海浪谱资料进行谱分析.以实测平均谱为靶谱,对随机波面进行模拟.得到模拟波面估计谱与实测谱极为相近,谱峰及谱峰频率都基本一致.说明利用模拟波面研究海浪具有代表性,它可以反映实测海浪的特征.利用实测海浪谱密度,统计波特征量的周期概率分布,得到理论周期概率密度与估计周期概率密度分布相符较好,且与模拟波面的波周期分布也较好的一致.利用Longuet-Higgins(1983)模型计算了波高-周期联合概率密度分布.得到变换高斯过程计算的波高与周期联合分布与实测情况基本相同,更好地描述了波高-周期联合概率密度分布.     

风浪波高和周期的联合概率密度分布

本文采用有代表性的44008美国国家浮标站2003年1～3月实测的海浪谱密度资料,选取三次大风过程进行风浪谱分析。通过对实测平均海浪谱与PM谱、JONSWAP谱及Torsethaugen谱的比较,得到PM谱拟和最好。然后用国际上最先进的随机波分析方法,根据协方差矩阵的循环嵌套技术,以实测平均谱与PM谱为靶谱,对随机波面进行模拟。得到由模拟波面统计的特征值及估计的谱与实测谱结果极为相近,谱峰及谱峰频率都基本一致。说明利用模拟波面研究海浪具有代表性,它可以反映实测海浪的特征。利用Longuet-Higgins(1983)模型计算波高-周期联合概率密度分布,得到变换高斯过程计算的波高、周期联合分布与实测情况基本相同,更好地描述了波高-周期联合概率密度分布。     

Parametric modelling of joint probability density distributions for steepness and asymmetry in deep water waves

Traditional wave steepness s = H/L does not define steep asymmetric waves uniquely. Three additional parameters characterising single zero-downcross waves in a time series are crest front steepness, vertical asymmetry factor and horizontal asymmetry factor. Parametric models for joint probability density distributions for deep water waves are presented. The joint distributions are for crest front steepness-wave height, vertical asymmetry factor-wave height, total wave steepness-wave height and wave height-wave period. The parametric models are estimated from zero-downcross analysis of wave data obtained from measurements at sea on the Norwegian continental shelf. The results of the analysis presented here can be used in the estimation of the probabilities of occurrence of steep asymmetric waves and breaking waves in deep water. Thus the results are useful for the practical naval architect and ocean engineer who are considering unusual events in the sea, the associated accidents or responses and the probability of occurrence of such events.     

Distribution of wave crests in a non-Gaussian sea

The sea elevation at a fixed point is modelled as a quadratic form of a vector valued Gaussian process with arbitrary mean. With this model, saddlepoint methods are used to approximate the mean upcrossing intensity with which the sea level crosses upwards at a certain height. This estimated intensity is further used to determine the probability distribution of wave crests. The use of saddlepoint technique is particularly important here because it can approximate the crest distribution without the need to perform simulations or use fitted distributions. Several numerical examples are given, including two with measured data. In the cases of real data, the results obtained with the saddlepoint technique are also compared with the results obtained with well known methods commonly used in the industry.     

Wave characteristic distributions for Gaussian waves—Wave-length, amplitude and steepness

In as tationary stochastic process the wave-length and amplitude are defined as the difference in time and height between a crest and the following trough. The distributions of these quantities are of great practical importance, but no closed form expressions are known at present. In previous papers we have presented an approximation which gives correct upper and lower bounds, regardless of the covariance structure under Gaussian assumptions. In this paper the suggested approximations are compared to two simpler approximations, one due to Cavanié et al. (1976) based on a cosine process and a new one, derived by replacing the model process by its regression curve.     

Calculating nonlinear wave crest exceedance probabilities using a Transformed Rayleigh method

This paper concerns the calculation of the wave crest height exceedance probabilities in fully nonlinear mixed sea states. The exceedance probabilities have been calculated by incorporating a fully nonlinear wave model into a Transformed Rayleigh method. This is an efficient approach to the calculation of wave crest exceedance probabilities and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The nonlinear mixed sea states studied include a swell dominated sea state, two wind sea dominated sea states, and two states of mixed wind sea and swell with comparable energy. The wave steepness influence and the finite water depth effects are also considered in the study. The accuracy and efficiency of the Transformed Rayleigh method are validated by comparing the results predicted using the method with those predicted by using the Monte Carlo simulation method, the theoretical Rayleigh method and some empirical formulas.     

THE DISTRIBUTION OF SIGNIFICANT CREST HEIGHTS OF SEA WAVES

Based on linear theory of sea waves, the height distribution of the intersections of wave surface with its envelope is derived. The distribution may be regarded as that of the significant crest heights under certain conditions. Some properties of this distribution are discussed in analogy to maxima theory. Data are found to be in good agreement with the theoretical curve.     

The distribution of zero-crossing wave heights and periods in a stationary sea state

Existing theoretical distributions of wave height and period do not reflect measured joint distributions from field data. A simulation methodology is introduced to retain the essential features of the theoretical background in Gaussian random noise but to avoid further compromising assumptions in the interpretation of height and period in the amplitude domain. A joint distribution can be associated directly with an empirical or measured variance spectrum. Spectral shape appears to dominate the detail of predicted joint distributions. There is generally a much sharper decay in probability levels at higher periods than is predicted by theoretical models. For Jonswap spectra, there is a dominant central ridge and a distinct bimodal structure in the joint distribution, features that are not evident in symmetric Gaussian spectral forms. The wave height distributions for Jonswap spectra differ little from the Rayleigh distribution, except at extreme wave heights where Rayleigh overpredicts. The period distributions are strongly sensitive to spectral shape. In the conditional distribution of periods, given the height, the asymptotic median period at extreme wave heights is significantly longer than the mean period for Jonswap spectra, but not for symmetric Gaussian forms.     

New theoretical aspects of statistical properties of narrow-banded random waves

By using a new concept of the discrete amplitude, we examine the statistical properties of narrow-banded random waves. The main results are as follows: (1) the wave height distribution follows the Rayleigh distribution in the case of an infinitely narrow-banded spectrum in the strict sense; (2) the discrete amplitudes, different from the crest heights, are distributed according to the Rayleigh distribution for arbitrary bandwidth spectra; (3) the statistical distribution of the gap length between the discrete amplitude and the crest is examined and derived theoretically. The derived distribution agrees well with the result of numerical simulations; (4) taking into account the gap length distribution, the probability density function of crest heights is derived, which deviates from the Rayleigh distribution.     

Run-up of long solitary waves of different polarities on a plane beach

We study the run-up of long solitary waves of different polarities on a beach in the case of composite bottom topography: a plane sloping beach transforms into a region of constant depth. We confirm that nonlinear wave deformation of positive polarity (wave crest) resulting in an increase in the wave steepness leads to a significant increase in the run-up height. It is shown that nonlinear effects are most strongly pronounced for the run-up of a wave with negative polarity (wave trough). In the latter case, the run-up height of such waves increases with their steepness and can exceed the amplitude of the incident wave.     

Retracking of Jason-1 Data

We present the results of retracking 18 cycles (15 from the Jason-TOPEX collinear period) of Jason-1 data. We used the retracking method of Rodriguez which simultaneously solves for all relevant waveform parameters using a 26 Gaussian model of the altimeter point target response. We find significant differences from the Jason-1 Project retracking in the key parameters of range and significant wave height (SWH) in the second version of the Project SGDRs. The differences from the Jason-1 data have a strong dependence on off-nadir angle and some dependence on SWH. The dependence of range on SWH is what is called sea state bias. The retracking technique also estimates surface skewness. For Jason-1 with its very clean waveforms we make the first direct estimates of the skewness effect on altimeter data. We believe that the differences found here and thus in overall sea surface height are the result of the standard project processing using a single Gaussian approximation to the Point Target Response (PTR) and not solving simultaneously for off nadir angle. We believe that the relatively large sea state bias errors estimated empirically for Jason-1 during the cal/val phase result from sensitivity of quantities, particularly SWH, in project GDRs to off nadir angle. The TOPEX-Jason-1 bias can be determined only when a full retracking of Jason-1 is done for the collinear period.     

Retracking of Jason-1 Data

We present the results of retracking 18 cycles (15 from the Jason-TOPEX collinear period) of Jason-1 data. We used the retracking method of Rodriguez which simultaneously solves for all relevant waveform parameters using a 26 Gaussian model of the altimeter point target response. We find significant differences from the Jason-1 Project retracking in the key parameters of range and significant wave height (SWH) in the second version of the Project SGDRs. The differences from the Jason-1 data have a strong dependence on off-nadir angle and some dependence on SWH. The dependence of range on SWH is what is called sea state bias. The retracking technique also estimates surface skewness. For Jason-1 with its very clean waveforms we make the first direct estimates of the skewness effect on altimeter data. We believe that the differences found here and thus in overall sea surface height are the result of the standard project processing using a single Gaussian approximation to the Point Target Response (PTR) and not solving simultaneously for off nadir angle. We believe that the relatively large sea state bias errors estimated empirically for Jason-1 during the cal/val phase result from sensitivity of quantities, particularly SWH, in project GDRs to off nadir angle. The TOPEX-Jason-1 bias can be determined only when a full retracking of Jason-1 is done for the collinear period.     

Wave crest and trough distributions in a broad-banded directional wave field

It is well established that the modulational instability enhances the probability of occurrence for extreme events in long crested wave fields. Recent studies, however, have shown that the coexistence of directional wave components can reduce the effects related to the modulational instability. Here, numerical simulations of the Euler equations are used to investigate whether the modulational instability may produce significant deviations from second-order statistical properties of surface gravity waves when short crestness (i.e., directionality) is accounted for. The case of a broad-banded directional wave field (i.e. wind sea) is investigated. The analysis is concentrated on the wave crest and trough distribution. For completeness a comparison with a unidirectional wave field is presented also. Results will show that the distributions based on second-order theory provide a good estimate for the simulated crest and trough height also at low probability levels.     

基于多源遥感数据的日本海内波特征研究

日本海特殊的地理位置和复杂的地形使得该海域内波表征极为复杂,遥感是大范围观测内波的有效手段,已被广泛应用于内波的探测研究。本文利用MODIS、GF-1和ENVISAT ASAR遥感影像,开展了日本海内波特征研究。通过提取内波波峰线,生成了日本海内波空间分布图;获取了内波的波峰线长度和传播速度,并基于非线性薛定谔方程反演了内波振幅。研究结果表明,日本海内波分布范围宽广,不仅大陆架沿海区内波分布密集,深海盆地也探测到了大量内波;日本海北部45°N附近海域有少量内波出现,利用高分影像探测到朝鲜陆架浅海区有大量小尺度内波,大和海盆、大和隆起的西南部海域没有发现内波。日本海内波波峰线长达100多千米,深海区的传播速度大于1 m/s;浅海区内波振幅约10 m左右,深海区可达60 m以上。     

On the distribution of crest to trough wave heights

In the present paper we derive the probability distribution function of crest to trough wave heights in a narrow-band, Gaussian stochastic process. It is shown that the distribution function is a one-parameter Rayleigh distribution where the parameter is expressed in terms of the correlation function of the given process. Comparison based on correlation values obtained via sea wave spectra indicate that the derived distribution function agrees well with observed data.     

Nonlinear effects of the distribution of amplitudes of sea waves

The effect of nonlinearities, such as wave-breaking and vertical asymmetry associated with sea waves, on the distribution of wave amplitudes is explored. Semiclosed theoretical expressions are derived to describe the distributions of breaking-limited crest and trough amplitudes for Stokes-type nonlinear sea waves. These are compared with the conventional Rayleigh distribution appropriate to linear wave amplitudes. The construction of nonlinear wave envelopes with the fast Fourier transform technique is described. The technique can be utilized to enlarge the data base in empirical analyses of field records which typically contain limited information on amplitude characteristics. The theoretical distributions and the proposed data enlargement technique are demonstrated with the analysis of a nonlinear wave record.     

Statistical properties of successive wave heights and successive wave periods

Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Næss model [Næss A. On the distribution of crest to trough wave heights. Ocean Engineering (1985);12(3):221–34] and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights.Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregressive model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. Thus, the joint distribution of three successive wave heights can be obtained by combining conditional bivariate distributions. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation.Successive wave periods with corresponding wave heights exceeding a certain threshold have also been studied. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights, can be approximated by a multivariate Gaussian distribution.The theoretical distributions are compared with observed wave data obtained from field measurements in the central North Sea and in the Japan Sea, with laboratory data and numerical simulations.     

Low-Frequency Variations of the North Atlantic Sea Level Measured by TOPEX/Poseidon Altimetry

Eight years of sea surface height data derived from the TOPEX/Poseidon altimeter, are analyzed in order to identify long- and a-periodic behavior of the North Atlantic sea level. For easy interpolation, sea surface height data are converted into sea surface topography data using the geoid derived from EGM96 to degree 360. Principal Component Analysis is used to identify the most dominant spatial and temporal variations. In order to separate dominant periodic signals, a yearly and a half-yearly oscillation, as well as alias effects from imperfect ocean tide corrections, are estimated independently by a Harmonic Analysis and subtracted. The residuals are smoothed by a 90-day moving average filter and examined once again by a PCA, which identifies a low-frequency variation with a period of approximately 6-7 years and an amplitude of about 1 dm, as well as a large sea level change of partially more than ±1 dm within only few months. This sea level change can also be seen in yearly and seasonal sea level residuals. Furthermore, the analysis shows a significant sea level change in 1998 occurring almost over the whole North Atlantic, which is not clearly identified by the PCA. Similar results are obtained by analyzing sea surface temperature and sea level pressure data.     

Low-Frequency Variations of the North Atlantic Sea Level Measured by TOPEX/Poseidon Altimetry

Eight years of sea surface height data derived from the TOPEX/Poseidon altimeter, are analyzed in order to identify long- and a-periodic behavior of the North Atlantic sea level. For easy interpolation, sea surface height data are converted into sea surface topography data using the geoid derived from EGM96 to degree 360. Principal Component Analysis is used to identify the most dominant spatial and temporal variations. In order to separate dominant periodic signals, a yearly and a half-yearly oscillation, as well as alias effects from imperfect ocean tide corrections, are estimated independently by a Harmonic Analysis and subtracted. The residuals are smoothed by a 90-day moving average filter and examined once again by a PCA, which identifies a low-frequency variation with a period of approximately 6–7 years and an amplitude of about 1 dm, as well as a large sea level change of partially more than ±1 dm within only few months. This sea level change can also be seen in yearly and seasonal sea level residuals. Furthermore, the analysis shows a significant sea level change in 1998 occurring almost over the whole North Atlantic, which is not clearly identified by the PCA. Similar results are obtained by analyzing sea surface temperature and sea level pressure data.     

Eddy Detection Over Southern Indian Ocean Using TOPEX/POSEIDON Altimeter Data

Mesoscale eddies constitute the most energetic component of the variability of ocean currents. An attempt has been made for the detection of oceanic mesoscale eddy signatures over the Southern Indian Oceanic (SIO) regions using the dynamic topography derived from TOPEX/POSEIDON (T/P) altimeter data, by the signal processing technique, called matched filtering. After applying all the ocean and atmospheric corrections, data of a complete cycle of T/P over SIO has been used for detection of eddy signatures. The geoid undulations are removed from the data of corrected sea surface height from T/P and the resulting dynamic topographic data are passed through a matched filter designed to detect a generic eddy signature of Gaussian signal embedded in noise. The filter is optimized to detect eddies with amplitude 20 to 30 cm and diameters roughly 100?250 km. Out of all the analyzed data of T/P orbits over SIO a few examples are presented for brevity. Qualitative verification of eddies is done with some independent T/P sea level anomaly data over the region. The analysis shows that the matched filtering technique is most suitable for monitoring eddy signatures along the subsatellite track instantly over the remote and most hostile regions of the southern global oceans.