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A method is presented for the inversion of images of the sea surface taken by nautical radar into wave elevation that is specifically suitable for the prediction of the wave elevation outside the observation domain covered by the radar. By means of a beamwise analysis of the image obtained by a scanning radar, the image information is translated into wave elevation. Subsequently a 2D FFT is applied in order to obtain the directional wave components required for a linear propagation of the wave field. Assuming knowledge of the significant wave height, a method to obtain the correct scaling of the wave prediction is proposed. The proposed method is verified using synthetic radar images which are modelled by applying shadowing and tilt effect to synthesised short crested linear waves.

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... Also, maritime operation tasks such as cargo and personnel transfer, helicopter landing, high speed navigation, and small craft recovery would benefit from the prediction of workable time windows and/or extreme waves. The short-term (30-90 s) phase-resolved prediction of ocean waves is often referred to as deterministic sea wave prediction (DSWP) and has gathered increasing attention in recent years (e.g., Belmont et al. 2014;Naaijen and Wijaya 2014). The various proposed approaches typically fall under two schema: prediction by mathematical tools that utilize single point measurements, and predictions by models that utilize multipoint measurements at a distance and subsequent reconstruction of the surrounding wave field. ...

... An alternate approach to DSWP uses measurements throughout the wave field to reconstruct the two-dimensional sea and propagate toward a location of forecast interest. In this case, the predict-ahead time is a balance between computation time and wave group (Wu 2004) or phase velocities (Edgar et al. 2000), which can be demonstrated using space-time diagrams (Abusedra and Belmont 2011;Naaijen and Wijaya 2014;Qi et al. 2018b). There are several approaches to this type of DSWP, each of which requires some present knowledge of the wave field. ...

... Since then, notable improvements have been made in computing wave spectra for retrieval of statistical wave parameters (Ziemer and Gunther 1994;Borge et al. 1999;Liu et al. 2015). It is only within recent years that radar has been investigated for phase-resolved wave measurements (Dankert and Rosenthal 2004;Belmont et al. 2014;Naaijen and Wijaya 2014;Wijaya et al. 2015;Qi et al. 2016). ...

This work describes a phase-resolving wave-forecasting algorithm that is based on the assimilation of marine radar image time series. The algorithm is tested against synthetic data and field observations. The algorithm couples X-band marine radar observations with a phase-resolving wave model that uses the linear mild slope equations for reconstruction of water surface elevations over a large domain of O(km) and a prescribed time window of O(min). The reconstruction also enables wave-by-wave forecasting through forward propagation in space and time. Marine radar image time series provide the input wave observations through a previously given relationship between backscatter intensity and the radial component of the sea surface slope. The algorithm assimilates the wave slope information into the model via a best-fit wave source function at the boundary that minimizes the slope reconstruction error over an annular region at the outer ranges of the radar images. The wave model is then able to propagate the waves across a polar domain to a location of interest at nearer ranges. The constraints on the method for achieving real-time forecasting are identified, and the algorithm is verified against synthetic data and tested using field observations.

... These deterministic wave models can classically be divided into linear and nonlinear methods. As frequently pointed out (Köllisch et al., 2018;Klein et al., 2020;Law et al., 2020), linear models benefit from a shorter computation time, a critical feature for real-time prediction, and are thus often preferred for operational purposes (Morris et al., 1998;Belmont et al., 2006;Naaijen and Huijsmans, 2008;Naaijen et al., 2009;Abusedra and Belmont, 2011;Kosleck, 2013;Naaijen et al., 2014b). They offer rather satisfying results for moderate sea states and short propagation distances, or for prediction requiring information on quiescent periods only (Belmont et al., 2014). ...

... Most of the computational time is actually spent in processing the wave data collected with the technology available at sea, in order to provide a valid initial condition: this pre-processing step today represents the main obstacle to real-time prediction (Blondel et al., 2010;Köllisch et al., 2018). Much of the work conducted to overcome this challenge has focused on extracting wave information from sea surface elevation data, either through the use of wave buoys or radar imaging (Blondel et al., 2010;Naaijen et al., 2014b). However, to properly initialize a conventional HOS model, a snapshot of the sea surface elevation is not sufficient and additional independent information is required: classically, the velocity potential at the free surface. ...

Optimizing the production of wave energy converters using Model Predictive Control (MPC) requires a real-time, deterministic prediction of the waves arriving at the device. This study presents a new method for deterministic sea wave prediction, using the horizontal velocity profile over the water column as a boundary condition for a dedicated nonlinear wave model. However, direct measurement of the horizontal velocity component over the whole vertical column is hardly achievable at sea. A method to reconstruct this profile from measurement devices currently at use, such as ADCPs, is thus presented and evaluated. The performance of the prediction method itself is then tested using synthetic numerical data. First, the reconstruction of the horizontal velocity profile as a boundary condition is evaluated. Then, the whole prediction procedure is assessed. In both these stages, the simulations are based on synthetic numerical data and the outcomes are compared with numerical reference solutions. The results show that the method is promising enough to justify further investigation through wave tank experiments.

... The prediction time available is simply set by the time taken for waves to propagate from the location where they are measured to the prediction site. The relationship between the available prediction time, prediction space, and the properties of the measurement process can be described by the so-called space-time diagrams (Abusedra and Belmont 2011;Edgar et al. 2000;Naaijen et al. 2014;Qi et al. 2018) which yield all the necessary information. These diagrams show that there is always a user-defined compromise to be achieved between prediction time, prediction space, and accuracy. ...

... DSWP can generally be achieved in two different ways. The first approach (adopted, e.g., in Belmont et al. 2007;Naaijen and Wijaya 2014;Hilmer and Thornhill 2015) is to (i) calculate the spectral coefficients of the measured wave data (mainly using classical Fourier transform techniques), (ii) phase shift the obtained spectral coefficients by the prediction time and the angular frequency defined by the dispersion relationship, and (iii) spectral inversion of the shifted spectral coefficients to construct the predicted sea surface elevation. (When predicting wave-induced vessel motions, the frequency domain vessel models can use the spectral coefficients directly before inversion; e.g., Connell et al. 2015.) ...

A number of maritime operations can benefit from a short-term deterministic sea wave prediction (DSWP). Conventional X-band radars have recently been shown to provide a low-cost convenient source of two-dimensional wave profile information for DSWP purposes. However, such rotating radars typically introduce temporal smearing into the data, which introduces errors when traditional Fourier transform–based wave prediction methods are used. The authors report on a new approach for DSWP that avoids such errors. Furthermore, it is not susceptible to the condition number problems that arise with any form of direct or indirect inversion-based approaches. Extensive numerical analyses are conducted to illustrate the effect of the mixed space–time nature of the data on DSWP and the efficiency of the proposed technique to handle it.

... [13] used the 3D-FFT method combined with phase propagation to predict SSE, and found no significant correlation to a vessel mounted MRU. [25] describes a method for predicting SSE using a 2D-FFT. Simulations resulted in correlation values of R = 0.91 for real-time SSE, and R = 0.84 for T+135 second predictions. ...

... [29] used a neural network approach based on SNR, peak wave length, and mean wave period to improve significant wave height estimates. [25] proposes a scaling method using historical RMS ratios of the predicted sea surfaces to MRU measurements. ...

OceanWaveS GmbH has been developing a prototype system, based on standard non-coherent X-band navigational radars, capable of predicting future sea surface elevations. Combined with a vessel hydrodynamic simulator, this system will forecast ship motions. Applications for such a system include offshore operations, e.g. crane lifts, LNG, cargo and personnel transfers. The forecasts may be assimilated into automated control systems; e.g. floating wind turbines or dynamic positioning systems, or used within Decision Support Systems. This article presents correlation analysis results between the predicted sea surface elevations and vessel-mounted reference sensors for three independent sea trials. Despite neglecting vessel hydrodynamics, correlations of forecasts to measured references of 80% are achieved for T+60 seconds predictions for all sea trials. The prediction horizon is observed up to 180 seconds of forecast.

... In the present paper, we use non-coherent radar data in order to compute unscaled ship motions. As proposed in [25], a very straight-forward approach is used to obtain the correct scaling of the motion prediction: the ratio of the standard deviation of the prediction and the measurement of the ship motion, obtained over a running time history buffer, is used to finally scale the ship motion prediction. ...

... Here, k is again the 2D wave vector with θ the wave propagation direction: k = |k| (cos (θ ) , sin (θ )) As done by e.g. [24] and [25], we assume the radar back scatter is related to the tilt, the angle between the look direction and the normal to the sea surface, which is directly related to the derivative in radial direction of the sea surface. For small grazing angles, after linearization, and after removal of range dependency of the back scatter intensity, the wave related part of the radar back scatter can be modeled as follows: ...

For numerous offshore operations, wave induced vessel motions form a limitation for operability: Installation of wind turbines, removal and placements of top sites on/from jackets, landing of helicopters etc. can only be done safely in relatively benign wave conditions. In many cases the actually critical phase takes no more than some tens of seconds. An on-board prediction of vessel motions would enable crew to anticipate on these near future vessel motions and avoid dangerous situations resulting from large ship motions. This paper presents results from a field campaign in which non-coherent raw X-band navigation radar data was used as input for a procedure that inverts the radar data into a phase resolved estimation of the wave elevation. In combination with a wave propagation and vessel response model, this procedure can compute a prediction of phase resolved vessel motions, some tens of seconds up to minutes into the future, depending on radar range and sea state. We compare predictions obtained this way with actual measurements of a well intervention vessel that were obtained during a sea trial performed at the North Sea. It was concluded that the method results in very accurate predictions: correlations between 0.8–0.9 were obtained for predicted ship motions of/around the COG and the vertical motions of the helicopter deck.
Copyright © 2016 by ASME Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature
Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

... An example of this technology is the wave monitoring system WaMoS II introduced by Ziemer and Dittmer (1994) and at the base of the real-time wave prediction system developed by Reichert et al. (2010) within the On board Wave and Motion Estimator (OWME). A methodology based on 2D FFT is proposed by Naaijen and Wijaya (2014) to obtain a directional phase-resolved prediction of the wave elevation from radar data (additional information about the directional energy spectrum is required, e.g., from a wave buoy). A similar measurement could be used in wave-FF control. ...

Floating wind turbines rely on feedback-only control strategies to mitigate the negative effects of wave excitation. Improved power generation and lower fatigue loads can be achieved by including information about incoming waves in the turbine controller. In this paper, a wave-feedforward control strategy is developed and implemented in a 10 MW floating wind turbine. A linear model of the floating wind turbine is established and utilized to understand how wave excitation affects rotor speed and so power, as well as to show that collective pitch is suitable for reducing the effects of wave excitation. A feedforward controller is designed based on the inversion of the linear model, and a gain-scheduling algorithm is proposed to adapt the feedforward action as wind speed changes. The performance of the novel wave-feedforward controller is examined first by means of linear analysis and then with non-linear time-domain simulations in FAST. This paper proves that including some information about incoming waves in the turbine controller can play a crucial role in improving power quality and the turbine fatigue life. In particular, the proposed wave-feedforward control strategy achieves this goal complementing the industry-standard feedback pitch controller. Together with the wave-feedforward control strategy, this paper provides some insights about the response of floating wind turbines to collective-pitch control and waves, which could be useful in future control-design studies.

... The observation from Fig. 7 that the variance of the predicted wave elevation decreases with increasing τ is also due to the fact that for values of τ further into the future, the waves arriving at the radar location originate from further distances where the shadowing is more severe and the variance of the observation is lower; after sufficiently long time no wave information will be available at all anymore. Using one scaling factor α based on the variance of the entire observed image and the true variance of the waves as was proposed in Eq. (6), does not take into account this decreased visibility at large ranges from the radar and in fact does not even guarantee a correct variance at the radar for τ ¼ 0. An alternative which is supposed to be practical and feasible for real life applications is proposed by Naaijen and Wijaya (2014): a time history of the wave elevation at the radar position (e.g. by an auxiliary wave buoy or via recorded ship motions) and a time history of the predicted wave elevation can be recorded and used to calculate the variance of the true waves and the prediction. By taking the ratio of these variances, a scaling factor dedicated for the radar location can be obtained. ...

For advanced offshore engineering applications the prediction with available nautical X-band radars of phase-resolved incoming waves is very much desired. At present, such radars are already used to detect averaged characteristics of waves, such as the peak period, significant wave height, wave directions and currents. A deterministic prediction of individual waves in an area near the radar from remotely sensed spatial sea states needs a complete simulation scenario such as will be proposed here and illustrated for synthetic sea states and geometrically shadowed images as synthetic radar images. The slightly adjusted shadowed images are used in a dynamic averaging scenario as assimilation data for the ongoing dynamic simulation that evolves the waves towards the near-radar area where no information from the radar is available. The dynamic averaging and evolution scenario is rather robust, very efficient and produces qualitatively and quantitatively good results. For study cases of wind waves and multi-modal wind-swell seas, with a radar height of 5 times the significant wave height, the correlation between the simulated and the actual sea is found to be at least 90%; future waves can be predicted up to the physically maximal time horizon with an averaged correlation of more than 80%.

... For both studies the twodimensional representation of the wave field was obtained by correlating a limited number of input time traces of the wave elevation, recorded at a sparse set of locations, as suggested by Zhang et al. [23] and Janssen et al. [10]. A different approach, more directly related to the analysis method of X-band radar images of the surface elevation was used in [13] and [5], relying on 3D FFT techniques, widely accepted for retrieving statistical seas state properties from nautical radar and [17] using an alternative which is shown to be more suitable when deterministic (phase-resolved) wave sensing from nautical radar is aimed for. ...

We discuss the spatio-temporal domain, here referred to as the predictable zone, in which waves can be predicted deterministically based on an observation in a limited spatial or temporal domain. A key issue is whether the group or phase speed of the observed waves governs the extent of the predictable zone. We have addressed this issue again using linear wave theory on both computer-generated synthetic wave fields and laboratory experimental observations. We find that the group speed adequately indicates the predictable zone for forecasting horizons relevant for offshore and maritime applications.

Many offshore operations are carried out under restrictive operational limits due to uncertainties in the operating environment. Operators are looking for methods to enhance the operation envelopes and safety of their operations. With the advent of wave radar, optical and respective processing technology, it is now possible to measure incident phase-resolved wave-fields a distance away from a floating system. The incident wave-fields can be used to predict the response of the floating system ahead of time taken for the wave-fields to evolve into the floater location. In this paper, we demonstrate the concept via simulations of evolving wave-fields and the induced response of a generic floater. It is shown that the floating system response, and subsequent exceedance of the operational limits, can be predicted in advance. This methodology can help to reduce uncertainties related to the operating environment and the system response and forms a building block for operability decision support systems.

Floating wind turbines rely on feedback-only control strategies to mitigate the effects of wave excitation. Improved power generation and lower fatigue loads can be achieved by including information about the incoming waves into the wind turbine controller. In this paper, a wave-feedforward control strategy is developed and implemented in a 10 MW floating wind turbine. A linear model of the floating wind turbine is established and utilized to show how wave excitation affects the wind turbine rotor speed output, and that collective-pitch is an effective control input to reject the wave disturbance. Based on the inversion of the same model, a feedforward controller is designed, and its performance is examined by means of linear analysis. A gain-scheduling algorithm is proposed to adapt the feedforward action as the wind speed changes. Non-linear time-domain simulations prove that the proposed feedforward control strategy is an effective way of reducing rotor speed oscillations and structural fatigue loads caused by waves.

The encounter of extreme waves, extreme wave groups or of unfavourable wave sequences is a dangerous thread for ships and floating/fixed marine structures. The impact of extreme waves causes enormous forces whereas the encounter of an unfavourable wave sequence — not necessarily extreme waves — can arouse critical motions or even resonance, often leading to loss of cargo, ship and crew. Thus, besides a well thought-out maritime design, a system detecting critical incoming wave sequences in advance can help avoiding those dangerous situations, increasing the safety of sea transport or offshore operations. During the last two years (see [1] and [2]) a new system for decision support on board a ship or floating/fixed marine structure named CASH — C omputer A ided S hip H andling — has been introduced. The preceding papers showed the step wise development of the main components of the program code — 3D–WAVE FORECAST and 3D–SHIP MOTION FORECAST. These procedures provide a deterministic approach to predict the short-crested seas state within radar range of the ship, as well as resulting ship motions in 6 degrees of freedom. Both methods have been enhanced with special focus on the speed of calculation to ensure a just-in-time forecast. A newly developed component is the ADAPTIVE 3D-PRESSURE DISTRIBUTION. This method calculates the pressure distribution along the wetted surface of the ship hull using a newly developed stretching approach [3]. With the end of the joint project LaSSe — Loads on Ships in Seaway (funded by the German Government) the paper presents the CASH-system, giving the possibility to detect critical situations in advance. Thus not only decision support on board a cruising ship can be provided, but also time windows for offshore operations are identified well in advance.

A method to estimate sea surface elevation maps from marine radar image sequences is presented. This method is the extension of an existing inverse modeling technique to derive wave spectra from marine radar images, which assumes linear wave theory with temporal stationarity and spatial homogeneity of the observed sea surface elevation. The proposed technique to estimate wave elevation maps takes into account a modulation transfer function (MTF), which describes the radar imaging mechanisms at grazing incidence and horizontal polarization. This MTF is investigated and empirically determined by wave measurements and numerical simulations. The numerical simulations show that shadowing is the dominant effect in the radar imaging mechanism at grazing incidence and horizontal polarization. Further comparisons of wave spectra, as well as comparisons of the wave height probability distributions obtained by the wave elevation maps and the corresponding buoy measurements with the theoretical Rayleigh distribution, confirm the applicability of the proposed method.

The interaction of a plane wave and a slightly rough surface tilted away from a reference plane is investigated. Expressions for the scattered fields are obtained to second order for a perfectly conducting and a dielectric surface. In the limiting case of no tilt the fields agree with those of Rice. When the normal to the surface is rotated about the intersection between the incidence plane and the reference plane, the treatment yields important polarization effects and gives explicitly as a function of the tilt which irregularities on the surface contribute to the scattered power. Numerical results are obtained to investigate the relative magnitudes of the terms contributing to the cross sections.

Shadowing and modulation of microwave backscatter by ocean waves are
studied using coherent X-band radars. Two types of shadowing are
investigated: geometric shadowing (complete blockage of incident rays)
and partial shadowing (polarization-dependent diffraction combined with
weak scatterers). We point out that the frequency of occurrence of zero
signal-to-noise ratio samples cannot depend on the incident power level
or the polarization if geometric shadowing occurs but can if partial
shadowing exists. We then compare this behavior with observations, and
show that the data do not support the hypothesis that geometric
shadowing plays a significant role in low-grazing-angle microwave
scattering from the ocean surface. Furthermore, our data indicate that
partial shadowing only depends significantly on polarization for the
steep waves found near shorelines. We also study the modulation of
microwave backscatter by ocean waves using these data by looking at the
phase differences between received power and scatterer velocity. These
phase differences appear to be rather well explained by standard
composite surface theory at VV polarization, having values that are
positive looking up wave and negative looking down wave. For HH
polarization, however, breaking effects come into play and overshadow
composite surface effects of free waves. They cause the phase difference
to be near zero for up wave looks and near 180° for down-wave looks.
A simple model that involves both breaking and freely propagating waves
but does not include any shadowing effects is shown to account for
observed phase differences at both polarizations to within about
10°.

Directional seas are often modelled as a double summation of plane sinusoidal waves from different directions at a set of discrete frequencies. Unfortunately, this model is commonly used in a way which produces unrealistic standing wave phenomena and hence is not ergodic. Consequently, time averages of variables are not necessarily the same as space averages and averages over different realisations. The resulting point spectrum is randomly distributed about the target point spectrum as required, but the time history generated is only representative of a short record of the target sea. In this note, the basis of the phenomenon and its consequences for both wave tank and computer simulation work are described. Two alternative techniques of directional wave generation are discussed.Standing waves also occur near reflectors in the sea and test tanks; their effects on point and directional wave measurements are discussed.

An empirical inversion method is presented for determination of time series of ocean surface elevation maps from nautical radar-image sequences. The method is based on the determination of the surface tilt angle in antenna look direction at each pixel of the radar images. Thereby in situ sensors are not required. An external calibration is not necessary. A conventional nautical X-band radar, operating at grazing incidence and horizontal polarization in transmit and receive, is used as a sensor. Radar-image sequences, with their high spatial resolution and large coverage, offer a unique opportunity to derive and study individual waves and wave fields in space and time and therefore allow the measurement of individual wave parameters and wave groups. For validation of the inversion scheme, the significant wave heights derived from the inverted radar data sets and from colocated wave records are compared. It is shown that the accuracy of the radar-retrieved significant wave height is within the accuracy of the in situ sensors. Furthermore, a wave elevation time series is directly compared to a buoy record to show the capabilities of the proposed method.