Directional ocean wave spectra using buoy azimuth, pitch, and rollderived from magnetic field components

Buoy azimuth, pitch, and roll, when used with measurements of buoy vertical acceleration, can provide directional wave spectra. Earlier work, which considered effects of buoy hull magnetism, showed that azimuth can be determined from magnetic field measurements (K.E. Steele and J.C. Lau, 1986). This work is extended to show that buoy pitch and roll, and thus buoy slopes, can also be determined from the same measurements. These slopes can be determined from measurements of the magnetic field components inside the hull along two orthogonal axes parallel to the deck of a buoy. Algorithms are developed for estimation of azimuth, pitch, and roll angles using these measurements. The algorithms account for residual and induced hull magnetism. Azimuth, pitch, roll, and estimates of directional wave spectra are determined both from the magnetic field measurements and from a conventional wave measurement system on the same buoy. Comparisons show that estimates of directional spectra based on magnetometer-derived pitch and roll agree well     

海浪同化预报模型理论基础

将共轭变分同化方法应用于 LAGFD- WAM海浪数值模式 ,导出了海浪谱能量平衡方程的共轭方程以及风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用的相应共轭源函数 ,建立了海浪同化模型 ,数值计算仍采用特征线嵌入计算格式 ,为合成孔径雷达波谱反演资料和卫星高度计有效波高资料同化奠定理论基础     

Directional wave spectra measured with a cloverleaf buoy during ARSLOE

The cloverleaf buoy is designed to determine the directional wave spectra with high directional resolution by measuring the vertical acceleration, surface slope, and curvature of the ocean wave surface. This paper describes the properties of the directional wave spectra measured with the cloverleaf buoy during the Atlantic Remote Sensing Land Ocean Experiment (ARSLOE). It is shown that the directional wave spectra measured under relatively constant wind agree fairly well with the similarity spectrum reported previously, but some differences are found in the spectral parameters. The differences in the scale parameters are attributed to unstable atmospheric conditions, though reasonable explanations for those in the shape parameters are difficult now.     

Maximum entropy estimation of directional wave spectra from an array of wave probes

A procedure for estimating directional wave spectra from an array of wave probes based on the Maximum Entropy Method (MEM) is developed in the present paper. The MEM approach yields an angular spreading function at each frequency band consistent with the input cross-spectral density matrix. The method is evaluated using numerical simulations of directional sea states. The MEM is also used to analyze data obtained from the three-dimensional wave basin of the Hydraulics Laboratory, National Research Council of Canada. Finally, the MEM is compared with the Maximum Likelihood Method (MLM) and is shown to be a powerful tool for directional wave analysis.     

Wave direction analysis from data buoys

This paper describes a new procedure of directional wave analysis from pitch-roll buoy measurements. The two previous procedures adopted by the National Data Buoy Center (NDBC) [Steele, K. E., Lau, J. C. K. and Hsu, Y.-H. L. (1985) Theory and application of calibration techniques for an NDBC directional wave measurement buoy. IEEE Journal of Oceanic Engineering OE-10(4), 382-396; Steele, K. E., Teng, C.-C. and Wang, D. W. C. (1992) Wave direction measurements using pitch-roll buoys. Ocean Engineering 19(4), 349-375] are relevant to our formulations. In these two studies, an estimate for the total phase shift of the sea surface displacement/slope spectra from the measured buoy heave/pitch and heave/roll spectra was calculated either by a weighted average method or a maximum heave/pitch quad-spectrum method. These two formulations were based on a fundamental assumption of symmetric hull-mooring effect on pitch and roll motions, which will never be true in the oceans. In the present study we essentially incorporate the basic formulations of NDBC, but calculate two estimates for this total phase shift.Examples of directional wave analysis from data measured by a 3 m diameter discus buoy during Typhoon Herb are presented in this paper. This data set was also analyzed by the weighted average method of Steele et al. (1985) which yielded unsatisfactory results of wave directions during severe wave climates.     

High-frequency radar measurements of the ocean wave-directionalspectrum

Measurements of the ocean wave directional spectrum using a dual, high-frequency (HF) radar system are presented. A model-fitting technique is used to obtain wave measurements from the radar Doppler spectra. Over 100 h of data, collected NURWEC2 (Netherlands-UK Radar Wavebuoy Experimental Comparison), have been compared with measurements using a WAVEC directional wave buoy. The amplitude and directional characteristics of long-wave components at frequencies of 0.07-0.1 Hz in general show good agreement. Reasonable estimates of the directional spectrum across the whole frequency range are obtained when the assumptions of the model-fitting technique are appropriate. Remaining problems in radar measurement and difficulties in assessing accuracy are discussed     

Use of advanced directional wave spectra analysis methods

Frequency-dependent cross-spectral parameters for pitch-roll buoy data and parameters that describe directional wave spectra based on a directional Fourier series are developed by the National Data Buoy Center (NDBC) and other organizations that collect wave data. The World Meteorological Organization (WMO) specifies wave data product formats in its Wave Observation (FM 65 WAVEOB) code. Other organizations, such as the US Army Corps of Engineers Field Wave Gaging Program (FWGP), have similar specifications. A directional Fourier series has poor directional resolution compared with advanced methods such as those based on maximum likelihood and maximum entropy. Transformations are developed for applying the advanced methods and working with directional wave information stored in the WMO's FM 65 WAVEOB code, the FWGP's Wave Data Analysis Standard (WDAS) format, and similar codes and formats. Using the transformations, a directional Fourier series expansion method, a Maximum Likelihood Method (MLM), and a Maximum Entropy Method (MEM) are each applied to 115 sets of NDBC directional wave data. The MEM and MLM provide better directional resolution, but the MEM produces artificial double peaks. There are considerable differences for the three used methods. The developed transformation equations enable wave data users to apply the method that best suits their applications.     

Field intercomparison of nearshore directional wave sensors

Five measurement strategies (four in situ, one remote) for estimating directional wave spectra were intercompared in a 1980 experiment at the Coastal Engineering Research Center's Field Research Facility in Duck, NC. The systems included two pressure sensor/biaxial current meter combinations (different manufacturers), a triaxial acoustic current meter, an SXY gauge (square array of four pressure sensors), and a shore-based imaging radar. A detailed error analysis suggests sources for differences in estimated wave spectra from the different instruments; in general, they intercompare favorably. The major deviation among in situ gauges was associated with the triaxial acoustic current meter. Reliance on a vertical velocity measurement (instead of a direct pressure or sea-surface elevation measurement) can contribute additional uncertainty in directional spectral estimates. The imaging radar was successful in distinguishing multiple wave trains at the same frequency, which was not possible with the simple spectral estimation analysis applied to in situ data. However, the radar is not useful in providing accurate estimates of spectral density, nor in distinguishing multiple wave trains of different frequencies coming from the same direction. Selection of a measurement strategy for a particular need depends on the precise data requirements for that application. Although the five tested intercompared well, in practice not all are equally suitable for every application.     

Satellite wave measurements for coastal engineering applications

Measurements from the GEOSAT, ERS-1 and 2 and Topex/Poseidon satellites have now accumulated to over 15 years of global ocean wave and wind data. Extraction of wave height, wind speed and wave period from the satellite altimeters and directional wave spectra from the synthetic aperture radars are reviewed along with recent validation and calibration efforts. Applications of the data to a variety of problems illustrate the potential of satellite wave measurements.     

Statistical estimation of extreme ocean environments: The requirement for modelling directionality and other covariate effects

With increasing availability of good directional data, provision of directional estimates of extreme significant wave heights, in addition to the omni-directional estimates, is more common. However, interpretation of directional together with omni-directional design criteria is subject to inconsistency, even in design guidelines. In particular, omni-directional criteria are usually estimated ignoring directional effects. In this article, for data which exhibit directional effects, we show that a directional extreme value model generally explains the observed variation significantly better than a model which ignores directionality, and that omni-directional criteria developed from a directional model are different from those generated when directionality is not accounted for. We also show that omni-directional criteria derived from a directional model are more accurate and should be preferred in general over those based on models which ignore directional effects. We recommend use of directional extreme value models for estimation of both directional and omni-directional design criteria in future, when good directional data are available. If effects of other covariates (e.g. time or space) are suspected, we similarly recommend use of extreme value models which adequately capture sources of covariate variability for all design analysis.     

Estimation Approaches of ηUV,PUV and UV Directional Wave Spectra and Their Comparison

The observation and estimation of directional spectra of sea waves is one of the essential subjects of study of oceanic dynamics. On the basis of the irregular linear wave theory, estimation methods for i/UV, PUV and VV directional wave spectra are derived. By using ij and PUV data measured in-situ, directional wave spectra are estimated, meanwhile the virtues and defects of various spectra are comparied. This method provide a basis for the observations of sea waves.     

碟形浮标观测方向波谱误差分析及修正

改进了方向波谱的分析方法及噪声谱经验公式，使本法随测波环境及仪器特性自动修正经验参值，更易于实际应用。基于Maximum heave/pitch quad-spectrum method，由时域及频率域上的浮标动力反应数值计算，推求反应增益因子及相位延迟项，并进一步将其导入方向波谱计算，使其能修正资料浮标对波浪之轴不对称动态反应所造成的相位延迟不一致及主波向误差。经数值仿真验证，该方法的确能消减因资料浮标对波浪之轴不对称动态反应所造成的相位延迟及对主波向估算所造成之影响。应用花莲现场观测资料验证改良之主波向估算方法，得出是否考虑波浪运动与浮标运动间之振幅响应因子及相位延迟因子，所得之主波向的差异介于0－12℃之间。     

由压力、流速估计波浪方向谱数据处理方法

通过现场观测水底压力和矢量流速，可以估计海面波浪方向谱，此方法称为ＰＵＶ法。本文由不规则线性波浪理论和洪广文［２］方向谱概率模式结合导出ＰＵＶ估计谱的计算式，并针对实测数据受到干扰的问题、依据相关理论与经验，提出了谱估计的数据处理与修正方法     

Multidirectional wave transformation around detached breakwaters

The performance of the new wave diffraction feature of the shallow-water spectral model SWAN, particularly its ability to predict the multidirectional wave transformation around shore-parallel emerged breakwaters is examined using laboratory and field data. Comparison between model predictions and field measurements of directional spectra was used to identify the importance of various wave transformation processes in the evolution of the directional wave field. First, the model was evaluated against laboratory measurements of diffracted multidirectional waves around a breakwater shoulder. Excellent agreement between the model predictions and measurements was found for broad frequency and directional spectra. The performance of the model worsened with decreasing frequency and directional spread. Next, the performance of the model with regard to diffraction–refraction was assessed for directional wave spectra around detached breakwaters. Seven different field cases were considered: three wind–sea spectra with broad frequency and directional distributions, each coming from a different direction; two swell–sea bimodal spectra; and two swell spectra with narrow frequency and directional distributions. The new diffraction functionality in SWAN improved the prediction of wave heights around shore-parallel breakwaters. Processes such as beach reflection and wave transmission through breakwaters seem to have a significant role on transformation of swell waves behind the breakwaters. Bottom friction and wave–current interactions were less important, while the difference in frequency and directional distribution might be associated with seiching.     

Analysis of Wave Directional Spreading by Bayesian Parameter Estimation

A spatial array of wave gauges installed on an observatoion platform has been designed and arranged to measure the lo-cal features of winter monsoon directional waves off Taishi coast of Taiwan. A new method, named the Bayesian Parameter Estimation Method(BPEM) , is developed and adopted to determine the main direction and the directional spreading parame-ter of directional spectra. The BPEM could be considered as a regression analysis to find the maximum joint probability of parameters, which best approximates the observed data from the Bayesian viewpoint. The result of the analysis of field wave data demonstrates the highly dependency of the characteristics of normalized directional spreading on the wave age. The Mit-suyasu type empirical formula of directional spectrum is therefore modified to be representative of monsoon wave field. More-over, it is suggested that Smax could be expressed as a function of wave steepness. The values of Smax decrease with increas-ing steepness. Finally, a local directi     

风浪方向分布模式的比较

本文对目前常用的几种风浪方向分布模式进行了分析对比，进而根据由浪高仪阵列和ＥＮＤＥＣＯ９５６测波浮标在我国各海区测得的风浪方向谱，从波能方向分布、方向累积分布、方向分布的峰值和标准差四个方面，与光易恒、Ｈａｓｓｅｌｍａｎｎ和Ｄｏｎｅｌａｎ等分别由观测得到的经验方向分布以及文圣常等由解析方法得到的风浪方向谱进行了比较，结果表明：Ｄｏｎｅｌａｎ分布与实测结果比较一致，文圣常谱也较接近。此外，笔者在渤海由仪器阵列实测方向谱拟合得到的方向分布（改进的光易模式）与各地实测资料也比较符合。     

On the use of discrete seasonal and directional models for the estimation of extreme wave conditions

Extreme value theory is commonly used in offshore engineering to estimate extreme significant wave height. To justify the use of extreme value models it is of critical importance either to verify that the assumptions made by the models are satisfied by the data or to examine the effect violating model assumptions. An important assumption made in the derivation of extreme value models is that the data come from a stationary distribution. The distribution of significant wave height varies with both the direction of origin of a storm and the season it occurs in, violating the assumption of a stationary distribution. Extreme value models can be applied to analyse the data in discrete seasons or directional sectors over which the distribution can be considered approximately stationary. Previous studies have suggested that models which ignore seasonality or directionality are less accurate and will underestimate extremes. This study shows that in fact the opposite is true. Using realistic case studies, it is shown that estimates of extremes from non-seasonal models have a lower bias and variance than estimates from discrete seasonal models and that estimates from discrete seasonal models tend to be biased high. The results are also applicable to discrete directional models.     

Kalman filtering of vessel motions for ocean wave directional spectrum estimation

This paper proposes a high-speed iterative procedure for estimating the ocean wave directional spectrum from vessel motion data. It uses as input data, the measurements from motion sensors that are commonly available on dynamically positioned vessels and which may easily be installed on any ship. Because the necessary sensors are relatively inexpensive or may already be installed, it becomes an ideal solution to provide initial estimates to offline estimation procedures and to give spectral updates under quickly changing weather conditions. The Kalman filtering algorithm, for iterative harmonic detection, and frequency domain vessel response data are used in the estimation procedure. The results and conclusions are still based on synthesized data, but very promising.     

Detection of nonlinear waves and their contribution to ocean wave spectra Part I: Theoretical consideration

This is a Part I of a paper of nonlinearities of wind waves in the deep open ocean. First, considerations are given in order to verify the theoretical expression for bound waves from observed data. We compare the contribution of bound waves and double Bragg scattering to the second-order scattering, and we show that the contribution of bound waves is larger, and that bound waves can be detected by measuring the Doppler spectra of HF (high-frequency) radio wave scattering from the sea surface. Moreover, if the theory of the HF radio wave scattering from the sea surface is verified, so is the second-order perturbation theory for bound waves. Then, the contributions of bound waves to ocean wave spectra are investigated on the basis of the nonlinear theory. The bound waves are shown to modify frequency spectra and wave directional distributions at higher frequencies, and it is shown that although the modifications of frequency spectra are smaller for a two-dimensional field case than for a one-dimensional field case, they are not negligible at higher frequencies. On the other hand, the modifications of wave directional distributions are shown to be significant at higher frequencies. These discussions become significant only when bound wave predictions are verified in the open ocean. Consequently, it is shown that nonlinearities of water waves are important in considering both radio wave scattering from the sea surface and the detailed structures of ocean wave spectra at high frequencies.     

Measuring directional wave spectra using the 3D-ACM WAVE on fixedand taut-wire moorings

Field data were analyzed from a simultaneous deployment of two 3D-ACM WAVE instruments; one on a fixed seabed frame in the nearshore zone, and the other further offshore on a taut-wire mooring. An intercomparison of measurements of vertical and horizontal wave-orbital currents with pressures was used to evaluate the velocity sensor response under field conditions. Results using the fixed frame have validated the measured horizontal wave-orbital velocities, but found the vertical velocities to be less coherent with the pressure time-series. The influence of the instrument mooring system on the velocity measurements was investigated. The oscillation of the taut-wire mooring was found to influence the magnitude of the measured horizontal wave-orbital velocities and induce a phase lag between velocity and sea-surface elevation. Examination of other data from similar taut-wire moorings indicates a systematic relationship between the length of the mooring cable and the measured phase lag, consistent with the behavior of the mooring system considered as a forced, linearly damped oscillator. A comparison was made between the spectra of wave direction derived from both velocity and pressure data with that derived solely from velocity data. The results show a high coherence for the fixed mooring, but significant directional variability in the higher frequencies (>0.13 Hz) on the taut-wire mooring we employed, which we attribute to the mooring oscillation. The analysis further indicates that on taut-wire moorings, the spectra of wave direction should be resolved solely from velocity data. Using these findings, directional wave spectra were produced for the nearshore and offshore sites from 233 coincident events over a two-month period, and these data are presented in a time-averaged spectral format