Wave measurements by pressure transducers using artificial neural networks

Underwater ultrasonic acoustic transducers are frequently used in ocean wave measurements as they measure surface level using acoustic waves. However, their effectiveness can be severely affected in rough sea conditions, when bubbles generated by breaking waves interfere with their acoustic signals. When the seas are rough, one therefore often has to rely on a pressure transducer, which is generally used as a back-up for the acoustic wave gauge. A pressure transfer function is then used to obtain the surface wave information. Alternatively, the present study employed an artificial neural network to convert the pressure signal into significant wave height, significant wave period, maximum wave height, and spectral peakedness parameter using data obtained from various water depths. The results showed that, for water depths greater than 20 m, the wave parameters obtained from the artificial neural network were significantly closer to those obtained by the acoustic measurements than those obtained by using a linear pressure transfer function. Moreover, for a given water depth, the wave heights estimated by the network model from pressure data were not as good as those estimated by linear wave theory for large wave heights (above a 4 m significant wave height in this study). This can be improved if the training data set has more records with large wave heights.     

Estimation of Water Particle Velocities by Empirical Transfer Function

-In previous and this studies it appears that the linear and nonlinear wave theory can notaccurately and easily predict the water particle velocities.Therefore,different from the theoretical consider-ations,in this study we have attempted to determine the transfer function empirically.Laboratory experi-ments were performed under various wave conditions.The empirical formulas of the transfer function ofthe wave height,angular frequency and water particle velocity were obtained on the basis of these test databy dimensional analysis and regression analysis.In intermediate and deep water depth conditions,thetransfer function was only a function of a nondimensional parameter which is composed of the angular fre-quency,the depth of the velocity gauge under the still water level,water depth and the acceleration of grav-ity.Finally,the empirical formulas were compared with experimental data and observational data formpresent and Cavaleri's(1978)studies.The empirical formulas were found to be in sufficient correl     

Standing wave pressures due to regular and random waves on a vertical wall

The standing wave pressures due to laboratory-generated regular and random waves exerted on a vertical wall were measured in a wave flume. The standing wave pressures were measured at four relative depths of submergence on the test model. The regular wave test conditions ranged from intermediate to deep water conditions. The measured pressures due to regular waves were compared with results obtained using linear theory and third-order solution. In the case of random wave tests, the dynamic pressures due to the time histories of water surface elevation following the spectral characteristics of Pierson-Moskowitz and Bretschneider spectra were measured. These pressures are compared with simulated pressures obtained through the linear filter technique of Reid. The variation of pressure spectra along the depth are presented. In addition, comparison of spectral parameters, i.e. zeroth moment, spectral width parameter and narrowness parameter of measured and simulated pressure spectra, are reported and discussed. The behaviour of the coherence function between the wave elevation on the wall and the corresponding pressures is also discussed.     

Sub aerial random wave pressure and layer thickness on impermeable sea walls

Investigations on sub aerial wave pressures and layer thickness on plane impermeable and non-overtopping seawallns were carried out by using physical model studies. Seawalls with slopes of 1:3, 1:4 and 1:6 were used. JONSWAP spectrum with significant wave height, H_s from 0.08 to 0.2 m and peak periods, T_p from 1.5 to 6.0 s and a constant water depth of 0.7 m is used. Based on extensive measurements, empirical formulas for practical applications are proposed to predict the maximum, significant and mean sub aerial random wave pressure and layer thickness (thickness of water layer perpendicular to the still water level on the run-up zone) by using the surf similarity parameter, significant wave height and elevation on the sub aerial region as inputs. It is found that the maximum layer thickness is 1.11 times the significant layer thickness and maximum sub Arial wave pressure is 1.06 times the significant wave pressures. The predictive equations based on extensive measurements can be used for the design of non-overtopping seawalls.     

大糙率礁面影响下珊瑚礁海岸附近规则波演化及爬高试验研究

本文通过波浪水槽试验研究了大糙率礁面影响下波浪沿礁的演化和爬高规律，测试了一系列规则波工况并对比了光滑礁面和粗糙礁面的情况。结果分析表明：二次谐波是礁坪上透射波的重要组成成分，粗糙礁面使主频波和二次谐波减小，对更高阶波的影响不显著；相对礁坪水深是描述礁坪上波浪透射的关键参数，礁面从光滑变为粗糙时海岸附近透射系数显著减小，能量衰减系数平均增大了8%，但礁前反射系数与礁面糙率之间无明显关系；礁后岸滩爬高随着透射波高的增大而增长，最后拟合了本文试验条件下珊瑚礁大糙率礁面预测规则波爬高的关系式。     

Calibration/Validation of an Altimeter Wave Period Model and Application to TOPEX/Poseidon and Jason-1 Altimeters

The altimeter radar backscatter cross-section is known to be related to the ocean surface wave mean square slope statistics, linked to the mean surface acceleration variance according to the surface wave dispersion relationship. Since altimeter measurements also provide significant wave height estimates, the precedent reasoning was used to derive empirical altimeter wave period models by combining both significant wave height and radar backscatter cross-section measurements. This article follows such attempts to propose new algorithms to derive an altimeter mean wave period parameter using neural networks method. Two versions depending on the required inputs are presented. The first one makes use of Ku-band measurements only as done in previous studies, and the second one exploits the dual-frequency capability of modern altimeters to better account for local environmental conditions. Comparison with in situ measurements show high correlations which give confidence in the derived altimeter wave period parameter. It is further shown that improved mean wave characteristics can be obtained at global and local scales by using an objective interpolation scheme to handle relatively coarse altimeter sampling and that TOPEX/Poseidon and Jason-1 altimeters can be merged to provide altimeter mean wave period fields with a better resolution. Finally, altimeter mean wave period estimates are compared with the WaveWatch-III numerical wave model to illustrate their usefulness for wave models tuning and validation.     

Calibration/Validation of an Altimeter Wave Period Model and Application to TOPEX/Poseidon and Jason-1 Altimeters

The altimeter radar backscatter cross-section is known to be related to the ocean surface wave mean square slope statistics, linked to the mean surface acceleration variance according to the surface wave dispersion relationship. Since altimeter measurements also provide significant wave height estimates, the precedent reasoning was used to derive empirical altimeter wave period models by combining both significant wave height and radar backscatter cross-section measurements. This article follows such attempts to propose new algorithms to derive an altimeter mean wave period parameter using neural networks method. Two versions depending on the required inputs are presented. The first one makes use of Ku-band measurements only as done in previous studies, and the second one exploits the dual-frequency capability of modern altimeters to better account for local environmental conditions. Comparison with in situ measurements show high correlations which give confidence in the derived altimeter wave period parameter. It is further shown that improved mean wave characteristics can be obtained at global and local scales by using an objective interpolation scheme to handle relatively coarse altimeter sampling and that TOPEX/Poseidon and Jason-1 altimeters can be merged to provide altimeter mean wave period fields with a better resolution. Finally, altimeter mean wave period estimates are compared with the WaveWatch-III numerical wave model to illustrate their usefulness for wave models tuning and validation.     

Verification of sediment transport rate parameter on cross-shore sediment transport analysis

The sediment transport parameter helps determining the amount of sediment transport in cross-shore direction. The sediment transport parameter therefore, should represent the effect of necessary environmental factors involved in cross-shore beach profile formation. However, all the previous studies carried out for defining shape parameter consider the parameter as a calibration value. The aim of this study is to add the effect of wave climate and grain size characteristics in the definition of transport rate parameter and thus witness their influence on the parameter. This is achieved by taking the difference in between “the equilibrium wave energy dissipation rate” and “the wave energy dissipation rate” to generate a definition for the bulk of sediment, dislocating within a given time interval until the beach tends reach an equilibrium conditions. The result yields that empirical definition of transport rate parameter primarily governs the time response of the beach profile. Smaller transport rate value gives a longer elapsed time before equilibrium is attained on the beach profile. It is shown that any significant change in sediment diameter or wave climate proportionally increases the value of the shape parameter. However, the effect of change in wave height or period on sediment transport parameter is not as credit to as mean sediment characteristics.     

Effects of currents on interpretation of sub-surface pressure spectra

Ocean waves are often measured using sub-surface pressure transducers. The transfer function, relating pressure fluctuations to variations in water-surface elevation, is usually based on linear wave theory, with an empirical correction factor being applied to account for non-linearities.This paper is concerned with the determination of surface-elevation spectra from pressures recorded beneath irregular waves travelling on a current. Predicted spectra are compared with spectral densities calculated from measurements using a surface-piercing wave gauge. Results show that significant errors arise if the Doppler effect, associated with the presence of the current, is ignored. The importance of selecting appropriate values of the empirical correction factor is also demonstrated.     

Wave modelling in the vicinity of submerged breakwaters

This paper describes a simple method for modelling wave breaking over submerged structures, with the view of using such modelling approach in a coastal area morphodynamic modelling system.A dominant mechanism for dissipating wave energy over a submerged breakwater is depth-limited wave breaking. Available models for energy dissipation due to wave breaking are developed for beaches (gentle slopes) and require further modifications to model wave breaking over submerged breakwaters.In this paper, wave breaking is split into two parts, namely: 1) depth-limited breaking modelled using Battjes and Janssen's (1978) theory [Battjes, J.A. and Jannsen, J.P.F.M. (1978). Energy loss and setup due to breaking of random waves. Proceedings of the 16th Int. Conf. Coast. Eng., Hamburg, Germany, pp. 569-587.] and 2) steepness limited breaking modelled using an integrated form of the Hasselmann's whitecapping dissipation term, commonly used in fully spectral wind–wave models. The parameter γ₂, governing the maximum wave height at incipient breaking (H_max = γ₂d) is used as calibration factor to tune numerical model results to selected laboratory measurements. It is found that γ₂ varies mainly with the relative submergence depth (ratio of submergence depth at breakwater crest to significant wave height), and a simple relationship is proposed. It is shown that the transmission coefficients obtained using this approach compare favourably with those calculated using published empirical expressions.     

Directional spread parameter at intermediate water depth

The characteristics of directional spread parameters at intermediate water depth are investigated based on a cosine power ‘2s' directional spreading model. This is based on wave measurements carried out using a Datawell directional waverider buoy in 23 m water depth. An empirical equation for the frequency dependent directional spreading parameter is presented. Directional spreading function estimated based on the Maximum Entropy Method is compared with those obtained using a cosine power ‘2s' parameter model. A set of empirical equations relating the directional spreading parameter corresponding to the peak of wave spectrum to other wave parameters like significant wave height and period are obtained. It shows that the wave directional spreading at peak wave frequency can be related to the non-linearity parameter, which allows estimation of directional spreading without reference to wind information.     

A Practical bi-parameter formula of gas transfer velocity depending on wave states

The parameter that describes the kinetics of the air-sea exchange of a poorly soluble gas is the gas transfer velocity which is often parameterized as a function of wind speed. Both theoretical and experimental studies suggest that wind waves and their breaking can significantly enhance the gas exchange at the air-sea interface. A relationship between gas transfer velocity and a turbulent Reynolds number related to wind waves and their breaking is proposed based on field observations and drag coefficient formulation. The proposed relationship can be further simplified as a function of the product of wind speed and significant wave height. It is shown that this bi-parameter formula agrees quantitatively with the wind speed based parameterizations under certain wave age conditions. The new gas transfer velocity attains its maximum under fully developed wave fields, in which it is roughly dependent on the square of wind speed. This study provides a practical approach to quantitatively determine the effect of waves on the estimation of air-sea gas fluxes with routine observational data.     

Numerical Simulation of Waves Generated by Seafloor Movements

Waves generated by vertical seafloor movements are simulated by use of a fully nonlinear two-dimensional numerical wave tank. In the souree region, the seafloor lifts to a designated height by a generation function. The numerical tests show that the linear theory is only valid for estimating the wave behaviors induced by the seafloor movements with a small amplitude, and the fully nonlinear numerical model should be adopted in the simulation of the wave generation by the large amplitude seafloor movements. Without the background surface waves, many numerical tests on the stable maximum elevations η0^max are carried out by beth the linear theory and the fully nonlinear model. The results of two models are compared and analyzed. For the fully nonlinear model, the influences of the amplitudes and the horizontal lengths on η^max are stronger than that of the characteristic duration times. Furthermore, results reveal that there are significant differences be- tween the linear theory and the fully nonlinear model. When the influences of the background surface waves are considered, the corresponding numerical analyses reveal that with the fully nonlinear model the η0^max near-linearly varies with the wave amplitudes of the surface waves, and the η0^max has significant dependences on the wave lengths and the wave phases of the surface waves. In addition, the differences between the linear theory and the fully nonlinear model are still obvious, and these differences are significantly affected by the wave parameters of the background surface waves, such as the wave amplitude, the wave length and the wave phase.     

Examination of empirical formulas for wave shoaling and breaking on steep slopes

Estimation of the wave height transformation of shoaling and breaking is essential for the nearshore hydrodynamics and the design of coastal structures. Many empirical formulas have been well recognized to the wave height transformation, but most of them were only applicable for gentle slopes. This paper reports the experimental results of wave shoaling and breaking over the steep slopes to examine the applicability of the previous empirical formulas. Two steep bottom slopes of 1/3 and 1/5, and one gentle slope of 1/10 were conducted in the present experiments. Experimental results show that the shoaling distance of steep slopes become short and the surface waves may be partially reflected from the steep bottom, thus the estimation of wave shoaling using the well-known previous formula did not conform completely to the experimental results. The previous empirical formulas for the wave breaking criteria were also examined, and the modified equations to the steep beaches were proposed in this work. A numerical model was finally adopted to calculate the wave height transformation in the surf zone by introducing the modified breaking index.     

Design estimates of surface wave interaction with compliant deepwater platforms

The extreme behavior of surface waves as they encounter and pass compliant deepwater platforms is an important class of problems for offshore engineers attempting to specify the platform deck elevation. In this study analytical expressions for the probability density and cumulative distribution functions that utilize empirical coefficients in an attempt to accurately model surface wave runup and airgap problems are presented. The analysis focuses upon interpreting the tails of the measured data histograms using two parameter Weibull distribution models. The appropriate empirical constants, assumed to be solely dependent upon the significant wave height, were evaluated and compared for all the test data. Based upon a small select set of data, for a mini-TLP and two Spar platforms, the airgap problem was found to be adequately modeled using a Rayleigh distribution. Further, for the seven seastates analyzed, the Weibull shape parameter was nearly constant and the data confirmed that the exclusive fit of the scale parameter assuming dependence only on the significant wave height was a reasonable approach for modeling the wave runup. Finally, by combining these models with a Poisson return model for each storm the associated reliability estimates for various deck heights were estimated.     

一个新的热带气旋参数调整方案

基于前人的统计经验公式和现有的实测资料,尤其是详实的热带气旋中心气压资料,对热带气旋的最大风速半径的确定提出一个新的调整方案,使之能较好反映热带气旋风场.比较结果表明,所计算的海浪场与实测资料吻合较好.     

Wave reflection by a vertical wall with a horizontal submerged porous plate

By applying the linear water wave theory and the eigenfunction expansion method, the wave reflection by a vertical wall with a horizontal submerged porous plate is investigated in this paper. The numerical results, concerning the effects of the dimensionless plate length, the relative water depth, and the porous effect parameter of the plate on the wave loads on the plate and the wave height near the wall as well as the reflection coefficient, are discussed. It is found that the submerged plate increases the complexity of the phenomenon related to the wave reflection and refraction in the close region of the wall, and leads to the occurrence of the phenomenon of wave trapping. The results indicate that there may exist a process of focusing wave energy near the wall for small dimensionless porous effect parameters, whereas the increase of the dimensionless porous effect parameter decreases gradually the wave height until setdown occurs. The behavior of a larger plate with proper porosity is similar to that of a wave absorber which can significantly suppress not only the wave height above the plate but also the reflection waves. The ability of the porous plate to reduce the wave height on the wall surface is, in general, directly proportional to the dimensionless plate length and may be strongest for a proper value of the dimensionless porous effect parameter. It is also demonstrated that the wave loads on a porous plate are smaller than those on an impermeable plate.     

Probabilistic Distribution of the Maximum Wave Heigh

A new method of treating maximum wave height as a random variable in reliability analysis of breakwater caissons is proposed. The maximum wave height is expressed as the significant wave height multiplied by the so-called wave height ratio. The proposed wave height ratio is a type of transfer function from the significant wave height to the maximum wave height. Under the condition of a breaking wave, the ratio is intrinsically nonlinear. Therefore, the probability density function for the variable cannot be easily defined. In this study, however, it can be derived from the relationship between the maximum and significant waves in a nonbreaking environment. Some examples are shown to validate the derived probability density function for the wave ratio parameter. By introducing the wave height ratio into reliability analysis of caisson breakwater, the maximum wave height can be used as an independent and primary random variable, which means that the risk of caisson failure during its lifetime can be evaluated realistically.     

Probabilistic distribution of the maximum wave height

A new method of treating maximum wave height as a random variable in reliability analysis of breakwater caissons is proposed. The maximum wave height is expressed as the significant wave height multiplied by the so-called wave height ratio.The proposed wave height ratio is a type of transfer function from the significant wave height to the maximum wave height.Under the condition of a breaking wave, the ratio is intrinsically nonlinear. Therefore, the probability density function for the     

GPS buoy and pressure transducer results from the August 1990 Texaco Harvest Oil Platform Experiment

The Texaco Harvest Oil Platform Experiment took place August 22–28, 1990, off Point Conception, California. This platform has been designated as the NASA/JPL verification site for the TOPEX radar altimeter, which is to be launched in mid‐1992. The purpose of the experiment was to obtain measurements from GPS and other instrumentation that will be used at the site for the verification activities, and to determine the potential effects of the platform environment on the quality of the measurements. In conjunction with this experiment, a buoy equipped with a GPS receiver was floated in the vicinity of the platform for the purpose of measuring sea‐level change and waves relative to a reference receiver located on the platform. A pressure transducer installed at the site also provided sea‐level change and wave measurements relative to the platform. We present the data collection, processing, and analysis results comparing the GPS‐buoy and pressure transducer data. The GPS‐determined sea‐surface height measurements show 1.3‐cm agreement when compared with transducer‐determined heights taken over the same period of time. Low‐rate (15‐s) data were used to measure the change in sea‐level height due to tides, while high‐rate (1‐s) measurements provided temporal resolution sufficient for determining wave spectra.