Growth of Wind Waves with Fetch in the Sea of Japan under Winter Monsoon Investigated Using Data from Satellite Altimeters and Scatterometer

By using wind vector fields observed by the NASA Scatterometer (NSCAT) and significant wave heights observed by the TOPEX/POSEIDON and European Remote Sensing Satellite-2 (ERS-2) altimeters, one-dimensional fetch growth of wind waves has been investigated under conditions of strong wind and high waves caused by the East Asian winter monsoon in the Sea of Japan. The evolution of fetch-limited wind waves can be observed by the altimeters along their ground tracks. The fetch is estimated by using vector wind fields observed by NSCAT. The derived growth characteristics of wind waves are compared with empirical relationships between the non-dimensional fetch and significant wave height proposed by previous studies. Good agreement is discernible with Toba's fetch graph formula normalized by the friction velocity, while Wilson's well-known formula normalized by the wind speed at a height of 10 m tends to underestimate the wave height under such severe conditions of high wind and very long fetch. This discrepancy is explained by the wind-speed dependence of the drag coefficient. A simple correction to Wilson's formula for the high wind conditions is proposed and compared with the observed data.     

Downward transfer of momentum by wind-driven waves

A model for the downward transfer of wind momentum is derived for growing waves. It is shown that waves, which grow due to an uneven pressure distribution on the water surface or a wave-coherent surface shear stress have horizontal velocities out of phase with the surface elevation. Further, if the waves grow in the x-direction, while the motion is perhaps time-periodic at any fixed point, the Reynolds stresses associated with the organized motion are positive. This is in agreement with several field and laboratory measurements which were previously unexplained, and the new theory successfully links measured wave growth rates and measured sub-surface Reynolds stresses. Wave coherent air pressure (and/or surface shear stress) is shown to change the speed of wave propagation as well as inducing growth or decay. From air pressure variations that are in phase with the surface elevation, the influence on the waves is simply a phase speed increase. For pressure variations out of phase with surface elevation, both growth (or decay) and phase speed changes occur. The theory is initially developed for long waves, after which the velocity potential and dispersion relation for linear waves in arbitrary depth are given. The model enables a sounder model for the transfer to storm surges or currents of momentum from breaking waves in that it does not rely entirely on ad-hoc turbulent diffusion. Future models of atmosphere-ocean exchanges should also acknowledge that momentum is transferred partly by the organized wave motion, while other species, like heat and gasses, may rely totally on turbulent diffusion. The fact that growing wind waves do in fact not generally obey the dispersion relation for free waves may need to be considered in future wind wave development models.     

Triple diagram method for the prediction of wave height and period

Many formulations have been developed so far to predict the wave height and period from fetch length and wind blowing duration for a constant wind speed. This study aimed to predict wave parameters from fetch length and meteorological factors by using triple diagram methodology based on Kriging principles. Proposed model results were compared with Joint North Sea Wave Project (JONSWAP) model which is used so commonly in the ocean and coastal engineering studies. For the implementation of the methodology hourly wave and wind data were obtained from a buoy located in Lake Ontario. Numerical and graphical comparisons demonstrated that the proposed method outperforms the classical formulation.     

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.     

深水风浪破碎发生率与风速和风区的关系

根据于渤海中部采油平台测得的数据，结合实验室的测量，提出一种深水风浪破碎发生率与风速和风区关系的经验公式，与现已发表的少量海上测量结果相比较，此式符合良好。利用此式较好地解释了风浪破碎起始风速问题。     

台风移行速度与登陆角度对风暴潮的影响:一个理想模型数值实验

The effects of hurricane forward speed(V) and approach angle(θ) on storm surge are important and a systematic investigation covering possible and continuous ranges of these parameters has not been done before. Here we present such a study with a numerical experiment using the Finite Volume Community Ocean Model(FVCOM).The hurricane track is simplified as a straight line, such that V and θ fully define the motion of the hurricane. The maximum surge is contributed by both free waves and a forced storm surge wave moving with the hurricane.Among the free waves, Kelvin-type waves can only propagate in the down-coast direction. Simulations show that those waves can only have a significant positive storm surge when the hurricane velocity has a down-coast component. The optimal values of V and θ that maximize the storm surge in an idealized semi-circular ocean basin are functions of the bathymetry. For a constant bathymetry, the maximum surge occurs when the hurricane approaches the coast from the normal direction when the free wave generation is minimal; for a stepped bathymetry, the maximum surge occurs at a certain acute approach angle which maximizes the duration of persistent wind forcing; a step-like bathymetry with a sloped shelf is similar to the stepped bathymetry, with the added possibility of landfall resonance when the free and forced waves are moving at about the same velocity. For other cases, the storm surge is smaller, given other parameters(hurricane size, maximum wind speed, etc.)unchanged.     

Influence of the type of sea waves on the backscattered radar cross section at medium incidence angles

We consider the influence of the sea surface state on the backscattered radar cross section and the accuracy of the wind speed retrieval from the scatterometer data. We used a joint set of radars and buoys to determine the type of sea waves. Three types of sea waves were distinguished: developing wind waves, fully developed wind waves, and mixed sea. It is shown that the retrieval error of the near surface wind speed using a one-parameter algorithm is minimal in the case of fully developed wind waves. We compared these data with the results of radio-altimeter data analysis and showed that in both cases underestimation of the retrieval wind speed exists for developing wind waves and overestimation occurs for mixed sea. A variety of swell parameters (length of the dominating wave, swell height, swell age) significantly influence the backscattered radar cross section, leading to a growth in the mean square error of the retrieved wind speed during vertical sounding (radio-altimeter data), and only slightly influence the mean square error of the scatterometer data (medium incidence angles). It is necessary to include the information about the parameters of sea waves in the algorithms and take into account the regional wave properties to increase the accuracy of wind speed retrieval.     

两参量的海面阻力系数模式的探讨

从风浪的能量平衡方程出发，引进若干风要素与波要素以及波要素之间的定性关系，经演算可导出海面阻力系数（Ｃｐ）或是风速（Ｕ）和波龄（β）或是Ｕ和波高（Ｈ）的函数，然后沿用最小二乘法，终将得出４组１２个回归方程。当β（或β）或Ｈ为某一给定值，惟有Ｕ为唯一参量时，所提各式均可简化为非线性方程：ＣＤ＝ａ＋ｂ，Ｕ＋ｃ．Ｕ＾２；式中ａ，ｂ和ｃ为三个经验系数，就所检验的例子而言，本文的结果与实际的符合前人的为好。     

Discussion on the critical wind speed for wind-wave generation on the basis of shear-flow instability theory

Observed critical wind speeds for the generation of wind waves are compared with those derived from a shear-flow instability theory. The theory predicts that the critical wind speed depends on the fetch and, for the case of infinite fetch, it is 93 cm s^–1 at 30 cm above the mean water surface, which agrees well with observations at sufficiently large fetch. For water containing soap, the much larger critical wind speeds which are observed cannot be explained by the reduction of surface tension alone. A qualitative discussion suggests that the elasticity of surface films of soap can effectively increase the critical wind speed.     

世界大洋长历时局地风速和有效波高的统计与分析

本文基于美国海军测地卫星高度计提供的全球范围长历时局地平均风速和有效波高资料进行统计分析,结果表明,世界大洋长历时局地平均风速和有效波高有明显的相关性,其散布点系统地位于Wilson提出的深水充分成长风浪平均风速和有效波高经验曲线之上;并从能量叠加平衡方程,近似定量估计出大洋中长历时涌浪有效波高与局地平均风速的关系。     

Wave pattern induced by a moving atmospheric pressure disturbance

A moving low atmospheric pressure is a main feature of tropical cyclones, which can induce a system of forced water waves and is an important factor that cause water level rise during a storm. A numerical model based on the nonlinear shallow water equations is applied to study the forced waves caused by an atmospheric pressure disturbance moving with a constant velocity over water surface. The effects of the moving speed, the spatial scale and the central pressure drop of the pressure disturbance are discussed. The results show that the wave pattern caused by a moving low-pressure is highly related with its moving speed. The wave pattern undergoes a great change as the moving speed approaches the wave velocity in shallow water. When the moving speed is less than the wave velocity, the distribution of water surface elevation is nearly the same as that of the pressure disturbance, and the maximum of the water surface elevation is located at the center of pressure. When the moving speed is larger than the wave velocity, a triangle shaped wave pattern is formed with a depression occurs in front of the pressure center, and the maximum of the water surface elevation lags behind the center of pressure. As the moving speed increases, the maximum of the water surface elevation firstly increases and then decreases, which reaches a peak when the moving speed is close to the wave velocity. The maximum of water surface elevation is approximately in proportion to the central pressure drop, and slightly affected by the spatial scale of pressure disturbance. Both the central pressure drop and the spatial scale of the pressure disturbance do not significantly affect the forced wave pattern. However, a clear difference can be noticed on the ratio of the maximum water surface elevation in moving pressure situation to that in static situation, when the moving speed is close to the wave velocity. A pressure disturbance with smaller spatial scale and smaller central pressure drop will give a larger ratio when the moving speed is close to the wave velocity.     

CHGS method for numerical forecasting of typhoon waves——Ⅰ. Spectrum of waves in growing phase

Owing to the fact that the wind speed and direction of typhoon vary rapidly with time and space in typhoon fetch; the nearer to the typhoon eye the greater the wind velocity, and the shorter the wind fetch the smaller the wind time,as a result,the more difficult for the wind wave to fully grow. Hence.in typhoon wave numerical calculation it is impossible to use the model for a fully grown wave spectrum. Lately, the author et at. presented a CHGS method for numerical forecasting of typhoon waves, where a model for the growing wave spectrum was set up (see Eq. (2) in the text). The model involves a parameter indicating the growing degree of wind wave, i. e. ,the mean wave age β. When βvalue is small, the wave energy is chiefly concentrated near the peak frequency, so that the spectral peak gets high and steep; with the increase of β the spectral shape gradually gets lower and gentler; when β=Ⅰ, the wave fully grows, the growing spectrum becomes a fully grown P-M spectrum. The model also shows a spect     

Prediction of wave height and period for a constant wind velocity using the JONSWAP results

The results of the Joint North Sea Wave Project (JONSWAP), carried out in the North Sea in 1969, are used to derive formulae for significant wave height and wave period in terms of the wind speed (assumed constant) and fetch or duration. Values from the wave height formula are compared with those from the formulae of Bretschneider (1973) and Darbyshire (1963). It is proposed that the JONSWAP results be used for the prediction of fetch and duration limited waves formed under the action of the local wind field.     

Effect of air-sea temperature difference on the momentum exchange between air and sea for fetch-limited cases

Ｅｆｆｅｃｔ　ｏｆ　ａｉｒ－ｓｅａ　ｔｅｍｐｅｒａｔｕｒｅ　ｄｉｆｆｅｒｅｎｃｅ　ｏｎ　ｔｈｅ　ｍｏｍｅｎｔｕｍ　ｅｘｃｈａｎｇｅ　ｂｅｔｗｅｅｎ　ａｉｒ　ａｎｄ　ｓｅａ　ｆｏｒ　ｆｅｔｃｈ－ｌｉｍｉｔｅｄ　ｃａｓｅｓＣｈｅｎｇＺｈａｎａｎｄＷｕＳｈ...     

锋面通过台湾海峡时引起的快速成长波高推算

每年冬季因中国北方冷空气前缘东移出海南下而形成的锋面是造成台湾海峡内恶劣海况的原因之一，锋面的到临常引发快速增高的波浪，这种海况是目前作业化数值预报模式在操作上不易反映的。经验证明根据元素波模式推衍所得的面积风域法推算波浪，适合于推导季风期间海况的一种方法。本文将锋面期间风域是移动的特性结合面积风域理论，作为推算锋面抵达时推算波高的方法。本文提出加权风场内插法计算各时刻各网格点的风速，使得面积风域理论简化为在网格点上的离散计算。文中根据锋面期间实际观测数据计算波能传播速率与风能传播系数等参数，经由案例分析的结果显示这个离散化面积风域法可以合理地推算锋面期间快速成长的波高。     

Model analysis of the currents and wind waves in the Vistula Lagoon of the Baltic Sea

This paper considers the results of the numerical simulation of the steady currents and waves field structures in the Vistula Lagoon under constant wind forcing. The currents?? structure is essentially 3-dimensional. The direction of the near-shore drift is determined by the wind and shore orientation, but the currents involve two layers in the deeper part of the basin: the upper layer downwind current and the upwind compensative current in the underlying layer. The wind waves depend upon the wind speed, fetch, and depth until the wind speed is less than 6?C8 m/s. As the wind increases, the fetch??s dependence disappears. The wind height depends only on the wind??s magnitude, and, under stormy conditions (when the wind??s speed exceeds 15 m/s), the waves are limited by the water depth alone.     

A derivation of the scaling law, the power law and the scaling relation for fetch-limited wind waves using the renormalization group theory

A state of wind waves at a fetch is assumed to be transformed into another state of wind waves at a different fetch by the renormalization group transformation. The scaling laws for the covariance of water surface displacement and for the one-dimensional and two-dimensional spectrum and the power law for the growth relation are derived from the fact that the renormalization group transformation constitutes a semigroup. The scaling relation or the relation among the exponents of the power law is also derived, using the two assumptions that the renormalization group transformation is applicable to fetch-limited wind waves and that the saturated range exists, which implies that the directional distribution function of energy in the wave number region much larger than the peak wave number does not depend on wave number.     

Statistical Distribution of Surface Slope in A 3-D Ocean Wave Field

—A joint probability density function(PDF)for surface slopes in two arbitrary directions is de-rived on the basis of Longuet-Higgins's linear model for three-dimensional(3-D)random wave field.andthe correlation moments of surface slopes.as parameters in the PDF.are expressed in terms of directionalspectrum of ocean waves.So long as the directional spectrum model is given.these parameters are deter-mined.Since the directional spectrum models proposed so far are mostly parameterized by the wind speedand fetch.this allows for substituting these parameters with the wind speed and fetch.As an example.thewind speed and fetch are taken to be 14 m s and 200 km.and the Hasselmann and Donelan directionalspectra are.respectively.used to compute these parameters.Some novel results are obtained,One of the in-teresting results is that the variances of surface slope in downwind and cross-wind directions determined bythe Donelan directional spectra are close to those measured by Cox and Munk(1954).Some discussionsare m     

Resuspension patterns in the Baltic proper

Waves induce resuspension of surface sediments and contribute to the long-term mobilisation of particulate matter from erosion to accumulation bottoms. This has a major impact on the nutrient cycle in shallow seas by enhancing degradation, microbial production and recycling. The Baltic Sea represents such an area. The aim of this work is to analyse the spatial and temporal resuspension patterns in the Baltic Sea. To estimate the bottom friction velocity, modelled wave data are used in combination with data on grain size. This new data set is compared to a resuspension threshold of friction velocity to estimate the events of resuspension.The variation in bottom friction velocity, resuspension frequency and duration are related to wind climate, fetch, water depth and sediment type. Substantial resuspension can be found down to 40–60 m, with durations from one day to as much as two weeks. The highest winds in the area are highly anisotropic with a dominance of S-SW-W winds and the highest resuspension frequencies are found along the shallow eastern coasts. A seasonal pattern is observed with relatively high friction velocities and high resuspension frequencies during winter. There is also a variation depending on grain size, where sediments with fine and medium sand have a considerably higher percentage of resuspension events than bottoms with other dominant grain sizes. Five sub-areas are identified, characterised by different sediment types, resuspension and wind characteristics. If, in the future, wind speed increases as predicted, resuspension of sediments will also increase with effects on the nutrient cycle.     

Neural networks for wave forecasting

The physical process of generation of waves by wind is extremely complex, uncertain and not yet fully understood. Despite a variety of deterministic models presented to predict the heights and periods of waves from the characteristics of the generating wind, a large scope still exists to improve on the existing models or to provide alternatives to them. This paper explores the possibility of employing the relatively recent technique of neural networks for this purpose. A simple 3-layered feed forward type of network is developed to obtain the output of significant wave heights and average wave periods from the input of generating wind speeds. The network is trained with different algorithms and using three sets of data. The results show that an appropriately trained network could provide satisfactory results in open wider areas, in deep water and also when the sampling and prediction interval is large, such as a week. A proper choice of training patterns is found to be crucial in achieving adequate training.