Modeling ocean wave propagation under sea ice covers

Operational ocean wave models need to work globally, yet current ocean wave models can only treat ice covered regions crudely. The purpose of this paper is to provide a brief overview of ice effects on wave propagation and different research methodology used in studying these effects. Based on its proximity to land or sea, sea ice can be classified as： landfast ice zone, shear zone, and the marginal ice zone. All ice covers attenuate wave energy. Only long swells can penetrate deep into an ice cover. Being closest to open water, wave propagation in the marginal ice zone is the most complex to model. The physical appearance of sea ice in the marginal ice zone varies. Grease ice, pancake ice, brash ice, floe aggregates, and continuous ice sheet may be found in this zone at different times and locations. These types of ice are formed under different thermalmechanical forcing. There are three classic models that describe wave propagation through an idealized ice cover： mass loading, thin elastic plate, and viscous layer models. From physi cal arguments we may conjecture that mass loading model is suitable for disjoint aggregates of ice floes much smaller than the wavelength, thin elastic plate model is suitable for a con tinuous ice sheet, and the viscous layer model is suitable for grease ice. For different sea ice types we may need different wave ice interaction models. A recently proposed viscoelas tic model is able to synthesize all three classic models into one. Under suitable limiting conditions it converges to the three previous models. The complete theoretical framework for evaluating wave propagation through various ice covers need to be implemented in the operational ocean wave models. In this review, we introduce the sea ice types, previous wave ice interaction models, wave attenuation mechanisms,the methods to calculate wave reflection and transmission between different ice covers, and the effect of ice floe breaking on shaping the sea ice morphology. Laboratory experiments, field measurements and numerical simulations supporting the fundamental research in waveice interaction models are discussed. We conclude with some outlook of future research needs in this field.

Information System for Ocean Wave Resources and Its Application to Wave Power Utilization

An information system for ocean wave resources and its application to wave power utilization are introduced. It can manage, analyze and process the data in the monthly report of ocean wave observation records of the State Ocean Administration, and can provide various kinds of curves and numerical characters of statistics. This system has been put into utility in Guangzhou Institute of Energy Conversion (GIEC), the Chinese Academy of Sciences since 1996. An application example is given of the investigation and analysis on ocean wave resource of the Nan Ao Island, Guangdong Province, where a 100 kW onshore OWC (oscillating water column) wave power station will be built. The wave power distribution is obtained in different wave directions for different wave periods. It is found that 70 percent of the wave power comes from the direction of ENE, and more than 95 percent of the wave power is related with direction E. The average wave power density is about 3 kW/m, and more than 80 percent of the wave power is distributed in the wave periods of 4 second to 5 second. Based on the analysis of wave resources, a site on the east coast of the island and a design width of 20 m for the 100 kW station are suggested.

Spatial and temporal variation characteristics of ocean waves in the South China Sea during the boreal winter

The spatial and temporal variation characteristics of the waves in the South China Sea （SCS） in the boreal winter during the period of 1979/1980-2011/2012 have been investigated based on the European Centre for Medium-range Weather Forecasts interim （ERA-Interim） reanalysis dataset. The results show that the lead- ing mode of significant wave height anomalies （SWHA） in the SCS exhibits significant interannual variation and a decadal shift around the mid-1990s, and features a basin-wide pattern in the entire SCS with a center located in the west of the Luzon Strait. The decadal change from a weak regime to a strong regime is mainly associated with the enhancement of winter monsoon modulated by the Pacific decadal oscillation （PDO）. The interannual variation of the SWHA has a significant negative correlation with the E1 Nino Southern Oscillation （ENSO） in the same season and the preceding autumn. For a better understanding of the physi- cal mechanism between the SCS ocean waves and ENSO, further investigation is made by analyzing atmo- spheric circulation. The impact of the ENSO on the SWHA over the SCS is bridged by the East Asian winter monsoon and Pacific-East Asian teleconnection in the lower troposphere. During the E1 Nino （La Nino）, the anomalous Philippine Sea anticyclone （cyclone） dominates over the Western North Pacific, helps to weaken （enhance） East Asian winter monsoon and then emerges the negative （positive） SWHA in the SCS.

The Assessment of Ocean Wave Energy Along the Coasts of Taiwan

The wave energy resource around the coasts of Taiwan is investigated with wave buoy data covering a 3-year period （2007-2009）. Eleven study sites within the region bounded by the 21.5^°N-25.5°N latitudes and 118°E-122°E longitudes are selected for analysis. The monthly moving-average filter is used to obtain the low-frequency trend based on the available hourly data. After quantifying the wave power and annual wave energy, the substantial resource is the result of Penghu buoy station, which is at the northeastern side of Penghu Island in the Taiwan Strait. it is investigated that the Penghu sea area is determined to be the optimal place for wave energy production according to its abundant resource of northeasterly monsoon waves, sheltering of the Taiwan Island, operation and maintenance in terms of seasonal conditions, and constructability of wave power devices.

A joint method to retrieve directional ocean wave spectra from SAR and wave spectrometer data

This paper proposes a joint method to simultaneously retrieve wave spectra at dif ferent scales from spaceborne Synthetic Aperture Radar(SAR) and wave spectrometer data. The method combines the output from the two dif ferent sensors to overcome retrieval limitations that occur in some sea states. The wave spectrometer sensitivity coeffi cient is estimated using an ef fective signifi cant wave height(SWH), which is an average of SAR-derived and wave spectrometer-derived SWH. This averaging extends the area of the sea surface sampled by the nadir beam of the wave spectrometer to improve the accuracy of the estimated sensitivity coeffi cient in inhomogeneous sea states. Wave spectra are then retrieved from SAR data using wave spectrometer-derived spectra as fi rst guess spectra to complement the short waves lost in SAR data retrieval. In addition, the problem of 180° ambiguity in retrieved spectra is overcome using SAR imaginary cross spectra. Simulated data were used to validate the joint method. The simulations demonstrated that retrieved wave parameters, including SWH, peak wave length(PWL), and peak wave direction(PWD), agree well with reference parameters. Collocated data from ENVISAT advanced SAR(ASAR), the airborne wave spectrometer STORM, the PHAROS buoy, and the European Centre for Medium-Range Weather Forecasting(ECMWF) were then used to verify the proposed method. Wave parameters retrieved from STORM and two ASAR images were compared to buoy and ECMWF wave data. Most of the retrieved parameters were comparable to reference parameters. The results of this study show that the proposed joint retrieval method could be a valuable complement to traditional methods used to retrieve directional ocean wave spectra, particularly in inhomogeneous sea states.

Effect of non-Gaussian properties of the sea surface on the low-incidence radar backscatter and its inversion in terms of wave spectra by an ocean wave spectrometer

The principle of ocean wave spectrometers was first presented several decades ago to detect the directional wave spectrum with real-aperture radar(Jackson,1981). To invert wave spectra using an ocean wave spectrometer,for simplicity,the hydrodynamic forcing and wave-wave interaction effect are neglected and a Gaussian slope probability density function(pdf) is used to calculate the normalized backscattering cross-section( σ 0) of the ocean surface. However,the real sea surface is non-Gaussian. It is not known whether the non-Gaussian property of the sea surface will affect the performance of the inversion of the wave spectrum if following existing inversion steps and methods. In this paper,the pdf of the sea surface slope is expressed as a Gram-Charlier fourth-order expansion,which is quasi-Gaussian. The modulation transfer function(MTF) is derived for a non-Gaussian slope pdf. The effects of non-Gaussian properties of the sea surface slope on the inversion process and result are then studied in a simulation of the SWIM(Surface Waves Investigation and Monitoring) instrument configuration to be used on the CFOSAT(China-France Oceanography Satellite) mission. The simulation results show that the mean trend of σ 0 depends on the sea slope pdf,and the peakedness and skewness coefficients of the slope pdf affect the shape of the mean trend of σ 0 versus incidence and azimuth; owing to high resolution of σ 0 in the range direction,MTF obtained using the mean trend of σ 0 is almost as accurate as that set in the direct simulation; in the inversion,if ignoring the non-Gaussian assumption,the inversion performances for the wave spectrum decrease,as seen for an increase in the energy error of the inverted wave slope spectrum. However,the peak wavelength and wave direction are the same for inversions that consider and ignore the non-Gaussian property.

A temporal sliding procedure for ocean wave variational data assimilation and its application

For sequential performance of wave variational data assimilation, we proposed a temporal sliding method in which the temporal overlap is considered. The advantage of this method is that the initial wave spectrum of the optimization process is modified by the observations in latter and former times. This temporal sliding procedure is important for marginal region, such as the China seas, where the duration of assimilation effectiveness is 2-3 days. Experiments were performed in the whole course of Cyclone 9403 （Russ）. Around the cyclone center, the maximum value of wave elements did not change much by assimilation, because the extreme value was determined by wind energy input that was not yet optimized. In the area outside the cyclone center, this modification is evident especially for wind wave growth.

Empirical formula for wave length of ocean wave in finite depth water

In this paper, function characteristics of dispersion of ocean wave in finite depth water were analyzed systematically. The functional form of the fitting function is reasonably proposed, in which the parame- ters are optimally determined by the least square method (LSM). For infinitely deep and extremely shallow water, the fitting function fits strictly the dispersion to be fitted. A new technique is presented in application of LSM. An empirical formula with maximum error of less than 0.5% for computing wavelength in finite depth water is presented for practical applications.

Pioneering Proposal of Floating Type Ocean Wave Power Station

This serial research develops the unique ocean wave power station, which is composed of the floating type platform with a pair of the floats arranged at the interval of one wavelength and the counter-rotating type wave power unit whose runners are submerged in the seawater at the middle position of the platform. Such profiles make the flow velocity through the runners two times faster than that of the traditional fixed/caisson type OWC （oscillating water column）, that is, the runners may be able to get the dynamical energy eight times on the ideal. Besides, the runners counter-drive the inner and the outer armatures of the peculiar generator, respectively, and then the relative rotational speed is two times as fast as the speed of the single runner/armature. Such characteristics make the runner diameter large, namely the output higher, as you request, because the rotational moment of the power unit hardly act on the floating type platform. This paper, as the first step, discusses the platform behaviors at the normally oscillating wave. The platform behavior is affected by not only the length and the amplitude of the wave but also the relation between the weight of the platform and the buoyancy force of the floats.

A novel algorithm for ocean wave direction inversion from X-band radar images based on optical flow method

As one of the important sea state parameters for navigation safety and coastal resource management, the ocean wave direction represents the propagation direction of the wave. A novel algorithm based on an optical flow method is developed for the ocean wave direction inversion of the ocean wave fields imaged by the X-band radar continuously. The proposed algorithm utilizes the echo images received by the X-band wave monitoring radar to estimate the optical flow motion, and then the actual wave propagation direction can be obtained by taking a weighted average of the motion vector for each pixel. Compared with the traditional ocean wave direction inversion method based on frequency-domain, the novel algorithm is fully using a time-domain signal processing method without determination of a current velocity and a modulation transfer function（MTF）. In the meantime,the novel algorithm is simple, efficient and there is no need to do something more complicated here. Compared with traditional ocean wave direction inversion method, the ocean wave direction of derived by using this proposed method matches well with that measured by an in situ buoy nearby and the simulation data. These promising results demonstrate the efficiency and accuracy of the algorithm proposed in the paper.

Ocean wave diffraction in near-shore regions observed by Synthetic Aperture Radar

Observation and analysis of ocean wave diffraction in near-shore and near-island region was performed with Synthetic Aperture Radar （SAR） data, using an optimized retrieval method named parameterized first-guess spectrum retrieval method. The results retrieved from ERS-SAR and ENVISAT-ASAR images showed that, in the region sheltered by land jut, the energy of long waves is reduced by 10%-20% and that the propagation direction of long waves is changed due to the effect of topography. In the shadow zone behind the island, ocean wave can propagate along the seashore instead of perpendicular to the coastline, as shown by SAR images.

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.

Three-dimensional dynamic sea surface modeling based on ocean wave spectrum

In conventional marine seismic exploration data processing,the sea surface is usually treated as a horizontal free boundary.However,the sea surface is affected by wind and waves and there often exists dynamic small-range fluctuations.These dynamic fluctuations will change the energy propagation path and affect the final imaging results.In theoretical research,different sea surface conditions need to be described,so it is necessary to study the modeling method of dynamic undulating sea surface.Starting from the commonly used sea surface mathematical simulation methods,this paper mainly studies the realization process of simple harmonic wave and Gerstner wave sea surface simulation methods based on ocean wave spectrum,and compares their advantages and disadvantages.Aiming at the shortcomings of the simple harmonic method and Gerstner method in calculational speed and sea surface simulation effect,a method based on wave equation and using dynamic boundary conditions for sea surface simulation is proposed.The calculational speed of this method is much faster than the commonly used simple harmonic method and Gerstner wave method.In addition,this paper also compares the new method with the more commonly used higher-order spectral methods to show the characteristics of the improved wave equation method.

Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai （37°27.6′N, 122°15.1′ E）, China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths （v=0.3-3.5） is within the range of 0.9686 to 0.991 7. In addition, the Longuet-Higgins （1975） and Sun （1988） distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.

A new modulation transfer function for ocean wave spectra retrieval from X-band marine radar imagery

When imaging ocean surface waves by X-band marine radar, the radar backscatter from the sea surface is modulated by the long surface gravity waves. The modulation transfer function （MTF） comprises tilt, hydrodynamic, and shadowing modulations. A conventional linear MTF was derived using HH-polarized radar observations under conditions of deep water. In this study, we propose a new quadratic polynomial MTF based on W-polarized radar measurements taken from heterogeneous nearshore wave fields. This new MTF is obtained using a radar-observed image spectrum and in situ buoy-measured wave frequency spectrum. We validate the MTF by comparing peak and mean wave periods retrieved from X-band marine radar image sequences with those measured by the buoy. It is shown that the retrieval accuracies of peak and mean wave periods of the new MTF are better than the conventional MTF. The results also show that the bias and root mean square errors of the peak and mean wave periods of the new MTF are 0.05 and 0.88 s, and 0.32 and 0.53 s, respectively, while those of the conventional MTF are 0.61 and 0.98 s, and 1.39 and 1.48 s, respectively. Moreover, it is also shown that the retrieval results are insensitive to the coefficients in the proposed MTF.

Feasibility Limits for a Hybrid System with Ocean Wave and Ocean Current Power Plants in Southern Coast of Brazil

Some types of renewable energy have been experiencing rapid evolution in recent decades, notably among the energies associated with the oceans, such as wave and current energies. The development of new energy conversion technologies for these two forms of energy has been offering a large number of equipment configurations and plant geometries for energy conversion. This process can be implemented aiming at the result of feasibility studies in places with energy potentials, establishing minimum feasibility limits to be reached. This work aims to contribute in this sense with a feasibility study of a system with ocean wave power plants and with socio-current power plants to be operated on the southern coast of Brazil. This study evaluates a hybrid system with contributions from energy supplies obtained from wave plants and current plants, connected to the grid and supplying the demand of the municipalities in the North Coast region of the State of Rio Grande do Sul, the southernmost state of Brazil. The study was carried out with simulations with the Homer Legacy software, with some adaptations for the simulation of ocean wave plants and ocean current plants. The results indicate that the ocean wave power plants were viable in the vast majority of simulated scenarios, while the ocean current power plants were viable in the scenarios with more intense average ocean current speeds and with more expensive energy acquired from the interconnected system.

Flow around Wells Type Runner Installed in Floating Type Unique Ocean Wave Power Station

The authors have proposed the unique ocean wave power station, which is composed of the floating type platform with a pair of floats lining up at the interval of one wave pitch and the power unit where the runners are submerged at the middle of the platform. Such a profile can make the flow velocity at the runner twice faster than that of OWC （oscillating water column） type constructed adjacent to the seashore. The behavior of the platform in the wave has been reported, and this paper continuously investigates the effects of the runner casing on the runner work and the platform behavior. Besides, the flows around the Wells type, not only single runner but also tandem runners are investigated numerically. It was confirmed that the runner work attenuates the platform amplitude and the runner casing contributes to increase the output. The flow simulation suggests that the tandem runners may be appropriate for the floating type ocean wave power station to get enough output.

An assessment of global ocean wave energy resources over the last 45 a

Against the background of the current world facing an energy crisis,and human beings puzzled by the problems of environment and resources,developing clean energy sources becomes the inevitable choice to deal with a climate change and an energy shortage.A global ocean wave energy resource was reanalyzed by using ERA-40 wave reanalysis data 1957–2002 from European Centre for Medium-Range Weather Forecasts（ECMWF）.An effective significant wave height is defined in the development of wave energy resources（short as effective SWH）,and the total potential of wave energy is exploratively calculated.Synthetically considering a wave energy density,a wave energy level probability,the frequency of the effective SWH,the stability and long-term trend of wave energy density,a swell index and a wave energy storage,global ocean wave energy resources were reanalyzed and regionalized,providing reference to the development of wave energy resources such as wave power plant location,seawater desalination,heating,pumping.

Ocean Wave Simulation near the Seashore

In order to realize real-time simulation of ocean surface near the seashore, a new modeling method for shallow ocean wave and a level of detail （LOD） scheme are proposed in this paper. This modeling method describes ocean wave by modifying the sine wave, and gets wave direction at any ocean floor position by using wave number decomposition. The LOD scheme is proposed to realize real-time rendering of large-scale ocean surface by simplifying the ocean surface regular mesh based on real-time optimally adapting meshes （ROAM）. Experimental results show that this method can get fast rendering speed and realistic effect.

Evaluation of the simulation capability of the Wavewatch Ⅲ model for Pacific Ocean wave

Wave climate analysis and other applications for the Pacific Ocean require a reliable wave hindcast. Five source and sink term packages in the Wavewatch III model （v3.14 and v4.18） are compared and assessed in this study through comprehensive observations, including altimeter significant wave height, advanced synthetic aperture radar swell, and buoy wave parameters and spectrum. In addition to the evaluation of typically used integral parameters, the spectra partitioning method contributes to the detailed wave system and wave maturity validation. The modified performance evaluation method （PS） effectively reduces attribute numbers and facilitates the overall assessment. To avoid possible misleading results in the root mean square error-based validations, another indicator called HH （indicating the two authors） is also calculated to guarantee the consistency of the results. The widely used Tolman and Chalikov （TC） package is still generally efficient in determining the integral properties of wave spectra but is physically deficient in explaining the dissipation processes. The ST4 package performs well in overall wave parameters and significantly improves the accuracy of wave systems in the open ocean. Meanwhile, the newly published ST6 package is slightly better in determining swell energy variations. The two packages （ACC350 and BIA） obtained from Wavewatch III v3.14 exhibit large scatters at different sea states. The three most ideal packages are further examined in terms of reproducing wave- induced momentum flux from the perspective of transport. Stokes transport analysis indicates that ST4 is the closest to the NDBC-buoy-spectrum-based transport values, and TC and ST6 tend to overestimate and underestimate the transport magnitude, respectively, in swell mixed areas. This difference must be considered, particularly in air-wave-current coupling research and upper ocean analysis. The assessment results provide guidance for the selection of ST4 for use in a background Pacific Ocean hindcast for high wave climate research and China Sea swell type analysis.