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The workability of various types of operations offshore are largely affected by waves and wave induced motions. Examples are crew transfer from crew transfer vessels or service operation vessels to offshore wind turbines for maintenance, landing of helicopters in (navy) vessels and various crane operations. Over the recent years quite some effort has been put in technology aiming to provide a real time on-board prediction of approaching waves and wave induced vessel motions some minutes in advance. Enabling crew to anticipate, thus enhancing the safety and operability of these operations. This paper addresses the performance during a field test of the system as being under development by Next Ocean enabling such predictions, based on using an off-the-shelve (non-coherent) navigation radar system as a remote wave observer. Briefly summarizing (earlier publications on) the technical approach, focus will be on results obtained from a field test where the system was validated. Good agreements between ship motions as measured by an on-board motion reference unit and predictions obtained by the wave and motion prediction system during a field test on the North Sea near the Dutch coast on a 42 m patrol vessel will be shown in the results section, from which the usefulness of the system for operational decision support can be concluded.

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... The alternative approach relies on the direct resolution of the modulation mechanisms of the radar backscattered intensity by assuming its proportionality to the surface slope. In that case, the linear wave theory is also assumed to facilitate data processing (Dankert & Rosenthal 2004;Naaijen et al. 2018;Simpson et al. 2020). ...

... Gangeskar 2000) properties of radar images or on an external reference measurement (e.g. Naaijen et al. 2018). The determination of these coefficients is outside of the scope of the present paper, hence they are here assumed to be known. ...

... Using real radar data instead of data type 3 is thus expected to have a negative effect on the surface reconstruction accuracy. Nevertheless, algorithms based on this model have been shown to yield sound results using field measurements (Dankert & Rosenthal 2004;Naaijen et al. 2018). ...

Algorithms for reconstructing and predicting nonlinear ocean wave fields from remote measurements are presented. Three types of synthetic observations are used to quantify the influence of remote measurement modulation mechanisms on the algorithms’ performance. First, the observations correspond to randomly distributed surface elevations. Then, they are related to a marine radar model – the second type takes the wave shadowing modulation into account whereas the third one also includes the tilt modulation. The observations are numerically generated based on unidirectional waves of various steepness values. Linear and weakly nonlinear prediction algorithms based on analytical models are considered, as well as a highly nonlinear algorithm relying on the high-order spectral (HOS) method. Reconstructing surfaces from shadowed observations is found to have an impact limited to the non-visible regions, while tilt modulation affects the reconstruction more generally due to the indirect, more complex extraction of wave information. It is shown that the accuracy of the surface reconstruction mainly depends on the correct modelling of the wave shape nonlinearities. Modelling the nonlinear correction of the dispersion relation, in particular the frequency-dependent wave phase effects in the case of irregular waves, substantially improves the prediction. The suitability of the algorithms for severe wave conditions in finite depth and using non-perfect observations is assessed through wave tank experiments. It shows that only the third-order HOS solution predicts the right amplitude and phase of an emerging extreme wave, emphasizing the relevance of the corresponding physical modelling.

... RTWF is a considerable scientific and technical challenge, and the subject of a growing body of research, of which references [1][2][3][4][5][6][7][8][9][10][11][12] offer a broad enough variety of examples. While it has begun to attract the attention of industrial players, RTWF is not yet a technology mature enough to be applied in practice. ...

... In distributed approaches, measurements recorded in realtime allow the estimation of a finite number of wave modes [5][6][7][8][9], or serve as boundary conditions to propagate the solutions of differential equations in numerical simulations [10][11][12]. The physical model describing wave propagation can be linear [5][6][7] or non-linear [8][9][10][11][12][13]. ...

... In distributed approaches, measurements recorded in realtime allow the estimation of a finite number of wave modes [5][6][7][8][9], or serve as boundary conditions to propagate the solutions of differential equations in numerical simulations [10][11][12]. The physical model describing wave propagation can be linear [5][6][7] or non-linear [8][9][10][11][12][13]. As far as the remote sensing technology is concerned, X-band radars have attracted most of the research efforts so far [4,[6][7][8], although some researchers have attempted the use of a LiDAR [10] or an ADCP (Acoustic Doppler Current Profiler) [12]. ...

There is a growing interest in the applications of real-time wave forecasting (RTWF), which consists in predicting physical quantities directly related to waves, such as the free-surface elevation, wave loads, or the motion of a ship, from a few seconds to several minutes in advance, and using measurements updated in real time. Unlike comparable RTWF methods found in the literature, which are based on the solution of the physical wave propagation equations, the present approach, known as SBP (Spectrum-Based Predictor), adopts a rigorous probabilistic view on the wave prediction problem, based on well-established, standard oceanographic assumptions. This paper presents an application of the SBP method to real wave field data coming from a stereoscopic camera system. To the best of the authors’ knowledge, this is the first time stereo wave data are employed to test RTWF algorithms. The data, recorded at a location in Korea, in the Yellow Sea, present some considerable challenges, such as strong current in excess of 1 m/s, steep waves with substantial non-linear components, and large directional spread in the high-frequency range. With some adjustments to the original SBP approach to account for current, several prediction configurations are tested, showing excellent agreement between the experimental prediction performance curves, and those expected from the SBP theory. With an observation range in the order of 100m, and in the wave conditions studied, reasonably accurate predictions can be achieved up to 20s ahead (approximately 3.5 peak wave periods).

... Research on ODSSs [5][6][7][8][9] in recent decades has mainly focused on reducing the wave forecast uncertainty by, e.g., (1) developing high-fidelity wave forecast models [10] for forecasts of a few hours up to some days in advance; (2) calibrating the local alpha factor [1] with wave-measuring instruments deployed near the floater [11]; (3) measuring the wave field in front of the vessel and predicting the encountered waves through noncoherent or coherent radar systems or special cameras [8,[12][13][14]; and (4) estimating the wave spectrum by applying the ''ship as a wave buoy'' analogy [15,16] and predicting the sea state by extrapolation. Similar to the design of marine operations, such an ODSS predicts wave-induced vessel responses based on the presumed deterministic vessel condition in terms of, e.g., the load distribution and linearized viscous damping, which may deviate from the real condition at the operation execution phase. ...

... Similar to the design of marine operations, such an ODSS predicts wave-induced vessel responses based on the presumed deterministic vessel condition in terms of, e.g., the load distribution and linearized viscous damping, which may deviate from the real condition at the operation execution phase. These uncertainties of the vessel condition can significantly contribute to the errors of the predicted vessel motions and the consequent decision making [5,8,9]. Therefore, it is important to identify the on-site vessel conditions based on the information available on board and from the operation design phase. ...

... Eqs. (7) and (9) to (12) should be treated as a complete set of the measurement functions to calculate the predicted measurement vector +1, at each sigma point, while Eqs. (7) to (9) provide the procedure to calculate the measurement vector +1 . The measurement functions are very difficult to express in a compact mathematical formulation because (1) many different response characteristics can be included in the measurement space (e.g., and ); (2) it involves seakeeping simulations, rigid body motion transformations, derivative calculations, etc.; and (3) the applied RAOs again depend on the state and subsequent selection of the sigma points. ...

Wave-induced vessel motion prediction plays a critical role in ensuring safe marine operations. The operational limiting criteria can usually be calculated by applying presumed linearized vessel motion transfer functions based on the specified vessel loading condition, which may deviate from the real vessel condition when the operation is executed. Reducing the uncertainties of the onboard vessel loading condition can therefore improve the accuracy of vessel motion prediction and hence improve the safety and cost-efficiency for marine operations. However, parameters related to the onboard vessel loading condition can be difficult to measure directly, such as the center of gravity and moments of inertia. In addition, the hydrodynamic viscous damping terms are always subject to significant uncertainties and sometimes become critical for accurate vessel motion predictions. A very promising algorithm for the tuning of these important uncertain vessel parameters based on the unscented Kalman filter (UKF) that uses onboard vessel motion measurements and synchronous wave information was proposed and demonstrated previously by application to synthetic data. The present paper validates the UKF-based vessel seakeeping model tuning algorithm by considering measurements from model-scale seakeeping tests. Validation analyses demonstrate rational tuning results. The observed random errors and bias in relation to the measurement functions due to the applied simplification and linearization in the seakeeping simulations can lead to biased tuning. The importance of designing the state space and the measurement space is demonstrated by case studies. Due to the nonlinear relationship between the uncertain vessel parameters and the vessel motions, the tuning is shown to be sensitive to the mean state vector and selection of the surrounding sigma points.

... Les systèmes opérationnels fournissant des prédictions déterministes de champ de vagues en temps réel (comme ceux proposés par Hilmer & Thornhill (2015), Kusters et al. (2016) ou Naaijen et al. (2018)) utilisent des images de radars à bande X et des modèles physiques linéarisés. Ces choix proviennent de la capacités des radars nautiques à mesurer certaines propriétés locales de la surface océanique sur un large domaine (jusqu'à ∼ 3-4 km 2 ) autour de la structure sur laquelle ils sont montés, et de la contrainte du temps réel restreignant fortement l'utilisation v d'une modélisation complexe pour les processus physiques liés à la propagation vagues et à leur interaction avec la structure. ...

... Operational systems that provide real-time deterministic predictions of ocean wave fields (e.g., Hilmer & Thornhill, 2015;Kusters et al., 2016;Naaijen et al., 2018) rely on X-band radar images and linearized physical models. These choices come from the capacity of nautical radars to measure some local properties of the ocean surface over a large domain (up to ∼ 3-4 km 2 ) around the structure upon which they are mounted, and on the real-time constraint that strongly restrains from using a complex physical modeling of the wave propagation and wave/structure interaction processes. ...

... This way, radars are able to generate large spatio-temporal instantaneous datasets of wave elevations surrounding the structure upon which they are mounted, with a typical space resolution (limited by their range resolution) of about 5-10 m at sampling frequency 0.5-1 Hz. This technology has been implemented in commercial products such as WaMoS II developed by OceanWaveS GmbH TM (Hilmer & Thornhill, 2015), the prediction systems of Next Ocean TM (Naaijen et al., 2018), or FutureWaves TM (Kusters et al., 2016). A selection of radar images, together with the dispersion relation, can be used to estimate the directional wave spectrum. ...

Researches conducted in this thesis address the problem of deterministic prediction of ocean wave fields around a marine structure, a key parameter for the analysis and control of a vast range of offshore operations, on the basis ofdatasets acquired remotely by an optical sensor. Efforts focus on the inclusion, at low computational cost, of the modeling of nonlinear hydrodynamic phenomena, preserving the reliability the surface representation in case of severe sea state.A weakly nonlinear Lagrangian approach (ICWM), whose hydrodynamic properties are evaluated by inter-comparison with reference wave models, is selected for the description of the free surface. The prediction problem is then formulated as an inverse problem that aims at fitting the solution described by the wave model to observations, here composed of free surface elevation datasets generated by a synthetic, yet realistic, lidar sensor scanning the ocean surface at grazing angle. Predictions are then issued through the propagation in time and space of the parameterized wave model. The applicability of the methodology is validated using observations of both unidirectional and directional wave fields, obtained at differentinstants to compensate for their strong spatial non-uniformity. The relative performance comparison between ICWM and lower-order wave models highlights the improvements due to the modeling of wave nonlinearities, especially those pertaining to the correction of the dispersion relation. A demonstration of the usefulness of ICWM is then provided by meansof a procedure that is fully validated experimentally in a wave tank.

... Only a few methods are capable due to the contrary specifications of very fast calculation time and high accuracy at once. The fastest method but also simplest one is the linear theory, which has already been applied for wave prediction applications with promising findings [2,[7][8][9][10][11][12][13][14][15]. A Shipboard Routing Assistance system (SRA) based on the continuous ship's X-band radar measurements of the surrounding seaway were presented by Payer and Rathje [7]. ...

... They showed that for short forecast duration and small to moderate wave steepness, the accuracy of the linear approach is sufficient. In addition, Naaijen and Huijsmans [9,11] as well as Naaijen et al. [10,15] applied linear wave evolution equations for real time wave prediction and ship motion estimation in long as well as short crested waves concluding "that a 60s accurate forecast of wave elevation is very well feasible for all considered wave conditions and motion predictions are even more accurate". Due to the simpleness and robustness, the linear approach is an integral part of commercially available prediction system (e.g., FutureWaves TM [13,14], Next Ocean TM [6]). ...

... with W = Φ z | z=ζ as vertical velocity at the free surface. Using Equation (14) and Equation (15) as free surface boundary conditions, the boundary value problem is now exclusively related to the vertical velocity W(x, ζ(x, t), t) (in space domain) and the solution for W(x, ζ(x, t), t) in terms of ζ(x, t) and Ψ(x, t) can be determined by series expansion. The procedure proposed by West et al. [31] starts from the formal expression that the velocity potential Ψ(x, t) and vertical velocity W(x, ζ(x, t), t) can be represented as Taylor series expansion a z = 0. Assuming that Ψ(x, t) and ζ(x, t) are quantities of O(ζ n ), φ(x, t) and W(x, t) are expanded by perturbation series, with ζ as ordering parameter and M = m + 1 is the order of approximation of non-linearity. ...

This paper discusses the potential of deterministic wave prediction as one basic module for decision support of offshore operations. Therefore, methods of different complexity—the linear wave solution, the non-linear Schrödinger equation (NLSE) of two different orders and the high-order spectral method (HOSM)—are presented in terms of applicability and limitations of use. For this purpose, irregular sea states with varying parameters are addressed by numerical simulations as well as model tests in the controlled environment of a seakeeping basin. The irregular sea state investigations focuses on JONSWAP spectra with varying wave steepness and enhancement factor. In addition, the influence of the propagation distance as well as the forecast horizon is discussed. For the evaluation of the accuracy of the prediction, the surface similarity parameter is used, allowing an exact, quantitative validation of the results. Based on the results, the pros and cons of the different deterministic wave prediction methods are discussed. In conclusion, this paper shows that the classical NLSE is not applicable for deterministic wave prediction of arbitrary irregular sea states compared to the linear solution. However, the application of the exact linear dispersion operator within the linear dispersive part of the NLSE increased the accuracy of the prediction for small wave steepness significantly. In addition, it is shown that non-linear deterministic wave prediction based on second-order NLSE as well as HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance, with the HOSM providing a high accuracy over a wider range of applications.

... We note that there are currently no commercial operating solutions for this technology. Similar effort toward the representation of the ocean wave field has been made with X-band radars (or microwave radars): examples include Hilmer and Thornhill (2015), Kusters et al. (2016), Naaijen et al. (2018), Klein et al. (2020), and Zhang et al. (2022). When the LIDAR camera or X-band radar operating at grazing angles is mounted upon the structure or vessel, both are subject to a spatially uneven distribution of measurement points. ...

... In many marine engineering applications, it is often sufficient to use linear wave propagation models for a phase-resolved wave prediction (Hilmer and Thornhill 2015, Wijaya et al. 2015, Naaijen et al. 2018, Al-Ani et al. 2020. However, for a long-term forecast or nonlinear irregular sea states with a non-negligible wave steepness, nonlinear wave effects (particularly the nonlinear dispersion relation) are fairly significant; nonlinear models should become more appropriate to provide accurate real-time wave predictions (Guérin et al., 2019). ...

This paper details a comprehensive study of deterministic real-time wave forecasting in directional seas.
By using wave models on the basis of a Lagrangian description, a good balance was achieved between
computational efficiency and model accuracy. Nevertheless, due to the highly non-uniform spatial distribution
of data and the relatively small size of data in time inherent to remote optical measurements, the initial
conditions are determined through an optimization process, which is computationally demanding, especially
in multidirectional sea states. Accordingly, in order to offer a real-time system of wave prediction in the
case of multidirectional waves, we propose a simplified and succinct assimilation method for the process of
wave reconstruction. We also develop a three-dimensional spatio-temporal prediction zone where the future
evolution of wave fields can be estimated based on wave measurements. Lastly, we outline a tank-scale
experimental campaign conducted to mimic the measurements of a LIDAR in a real configuration. A comparison
of model performances with the experimental observations shows that in a multidirectional approach, it is
necessary to consider wave components in direction as well as in frequency to achieve nearly the same accuracy
as for unidirectional seas.

... Marine radars and LIDAR systems measure the wave field before waves approaching to vessel. Therefore, they can also be used as wave forecast information in a very short time ahead (e.g., up to few minutes) for real-time vessel and structural response prediction [25]. ...

... The nonlinearity of vessel roll motion is well-known due to the dominated nonlinear damping terms [35]. Therefore, it is often challenging to get acceptable quality of roll motion prediction when linear roll RAO is applied and the additional linearized damping term cannot be sufficiently tuned based on the full-scale measurements [10][11][12]25]. Better correlation between the extreme responses from the prediction and the measurement of roll motion has been normally observed. ...

Digital twins have attracted significant attention across different domains for decades. In the maritime and the energy industries, digital twins have been mainly used for system condition monitoring, project visualization, crew training, real-time decision making/support, and predictive maintenance based on onsite measurement data from onboard sensors. Such a digital twin normally presumes the vessel’s operational condition by assistance from sensors and engineering judgement. However, a vessel’s operational condition and loading state may shift quite often due to the frequently changing operational scenarios, tasks, and environmental conditions. In addition, the true vessel state (e.g., inertia distribution) may deviate from the intended one according to planning due to possible engineering errors. Even though there are sensors helping to monitor vessel condition such as draft monitoring systems and ballast systems, several important vessel parameters are difficult to measure directly, e.g., moment of inertia, center of gravity, and nonlinear hydrodynamic damping. This paper proposes a framework for monitoring vessel condition and providing decision support based on quantitative risk assessment, through a vessel state observer which is able to self-tune the important but uncertain vessel parameters by utilizing the available prior knowledge, vessel measurements, and information about the associated sea states. The tuned vessel parameters improve the information about the real-time vessel condition and consequently assist to improve the prediction accuracy of vessel seakeeping performance in the near future for the emerging wave conditions. Furthermore, the tuned results and the response prediction can then be applied to a decision support system, quantitatively evaluating potential risk and providing suggestions. The framework consists of 5 modules, i.e., wave data acquisition and processing, vessel data acquisition and processing, vessel seakeeping model tuning, real-time vessel motion and critical structural response prediction, and risk awareness and avoidance. Details of each module are described in the paper. The proposed framework can also assist in the development of autonomous ships.

... With the development in sensor technology and computational process capacity during the last two decades, many research-oriented onboard decision support systems (ODSS) for marine and offshore activities have been developed aiming at improving vessel motion predictions. Examples are: 1) SeaSense system ; 2) CASH system (Clauss et al., 2012); 3) OWME project (Onboard Wave and Motion Estimator) applying non-coherent WaMoS II radar (Dannenberg et al., 2010;Naaijen et al., 2016Naaijen et al., , 2018; 4) ESMF project (Environment and Ship Motion Forecasting) applying coherent wave radar systems Kusters et al., 2016;Alford et al., 2015). On-site full-scale tests have been performed for validation of the different proposed methods (Naaijen et al., 2016(Naaijen et al., , 2018Connell et al., 2015;Alford et al., 2015). ...

... Examples are: 1) SeaSense system ; 2) CASH system (Clauss et al., 2012); 3) OWME project (Onboard Wave and Motion Estimator) applying non-coherent WaMoS II radar (Dannenberg et al., 2010;Naaijen et al., 2016Naaijen et al., , 2018; 4) ESMF project (Environment and Ship Motion Forecasting) applying coherent wave radar systems Kusters et al., 2016;Alford et al., 2015). On-site full-scale tests have been performed for validation of the different proposed methods (Naaijen et al., 2016(Naaijen et al., , 2018Connell et al., 2015;Alford et al., 2015). Challenges on roll motion prediction based on the vessel being modelled as a linear transfer function, known as response amplitude operator (RAO), have been reported in all the relevant tests. ...

Vessel and wave hydrodynamics are fundamental for vessel motion prediction. Improving hydrodynamic model accuracy without compromising computational efficiency has always been of high interest for safe and costeffective marine operations. With continuous development of sensor technology and computational capacity, an improved digital twin concept for vessel motion prediction can be realized based on an onboard online adaptive hydrodynamic model. This article proposes and demonstrates a practical approach for tuning of important vessel hydrodynamic model parameters based on simulated onboard sensor data of vessel motion response. The algorithm relies fundamentally on spectral analysis, probabilistic modelling and the discrete Bayesian updating formula. All case studies show promising and reasonable tuning results. Sensitivities of the approach with respect to its key parameters were also studied. Sensor noise has been considered. The algorithm is found to be computationally efficient, robust and stable when tuning the values of hydrodynamic parameters and updating their uncertainties, within reasonable sensor noise levels.

... Methods for deterministic wave prediction have been developed using wave datasets obtained by LIDAR (Light Detection and Ranging) cameras (e.g., Grilli et al. 2011, Nouguier et al. 2013, Kabel et al. 2019, Desmars et al. 2020). An alternative to the LIDAR technique uses X-band radars (or microwave radars) to record observations of the sea surface elevation (e.g., Hilmer and Thornhill 2015, Kusters et al. 2016, Naaijen et al. 2018, Klein et al. 2020, Zhang et al. 2022a). Both LIDAR and X-band radar measurements, obtained by a structuremounted instrument with the grazing incidence angles of the beams, have inherent physical limitations, such as uneven spatial sampling. ...

Previous research on real-time deterministic sea wave prediction has generally focused on evaluating the accuracy and efficiency of short-term wave fields within a specific prediction zone. However, for a real-time wave prediction system, it is necessary to provide a continuous description of the ocean wave surface based on short-term prediction segments. In this regard, we have developed algorithms for continuous wave prediction in directional wave fields based on the ''practical" prediction zone. The practical prediction zone refers to the time interval available for generating a continuous wave forecast by excluding the reconstructed waves from the prediction zone proposed by Kim et al. (2023). We also introduce and discuss several important time factors, such as the update interval of the spatio-temporal wave dataset, the total computation time, and the length of the practical prediction zone. By gaining a deeper understanding of numerical modeling setups, we have established strategies to reduce computational costs, which are directly related to the accuracy of continuous wave prediction. In particular, the development of these strategies suggests guidance in specifying direction and frequency bandwidths for continuous wave prediction.

... Nevertheless, to the authors' best knowledge, only limited research and validation work have been conducted for predicting ship motion based on on-site wave-radar measurements so far. Next Ocean [7] and Futurewaves [8] are companies providing a commercial ship motion predictor based on wave-data measurements. Some research projects have been also reported [9]- [14]. ...

... One possibility is to employ data assimilation to reconstruct the free surface prior to making a prediction, as suggested by Desmars et al., 47 Qi et al. 48 or Naaijen et al. 49 who use sequences of images. Wang and Pan 50 have presented a framework that integrates data assimilation using ensemble Kalman filtering and HOS simulations for deterministic forecasting. ...

We develop a new methodology for the deterministic forecasting of directional ocean surface waves based on nonlinear frequency corrections. These frequency corrections can be pre-computed based on measured energy density spectra and, therefore, come at no additional computational cost compared to linear theory. The nonlinear forecasting methodology is tested on highly nonlinear synthetically generated seas with a variety of values of average steepness and directional spreading and is shown to consistently outperform a linear forecast.

... Stredulinsky D C addressed the issue of performance during a field test of the system as being under development by Next Ocean enabling such predictions, based on using an off-the-shelf (non-coherent) navigation radar system as a remote wave observer. This prediction system was used in a field test on the North Sea near the Dutch coast on a 42 m patrol vessel [24]. However, absolute measurement is mostly used in the production and manufacture of grating measurement, medical imaging, and small machinery industry, and not much research has been conducted in the field of ship measurement [25][26][27][28][29][30]. ...

Due to the fact that there is no static reference point in ocean space, relative measurement sensors such as laser sensors cannot be applied to the measurement of ship motion. In order to collect the motion signal of a ship in the ocean more accurately, an absolute measurement method for the motion of a ship is proposed. Firstly, the acceleration signal in the heave direction of the ship is obtained by using an acceleration sensor; secondly, the time–frequency domain integration algorithm is used to avoid the problem of the quadratic trend item and the influence of the low-frequency signal, and the ship’s heave displacement value is obtained by integration; finally, the displacement signal measured by the laser sensor and the integrated displacement signal of the acceleration sensor are compared with each other to verify the effectiveness of the absolute measurement of the heave displacement of the ship based on the acceleration sensor. At the same time, an angle sensor is used to measure the roll angle and pitch angle in the motion of the ship, form an absolute measurement system for the motion of the ship, and verify that the measurement points are arranged on the ship, which proves that the system can collect data from the ship in sea areas far from the coast. Motion signals are more advantageous.

... After post-processing, ship navigation radar measurements (see Chapter 6.1) can also be used in combination with wave propagation and ship motion theory to predict ship motions in real time, for instance the next few minutes (Alford et al. (2015), Connell et al. (2015), Naaijen (2018); Naaijen et al. (2018)). This can be used in operation to identify a quiet period for lifting or the need to reduce speed. ...

Committee Mandate
Concern for descriptions of the ocean environment, especially with respect to wave, current and wind, in deep and shallow waters, and ice, as a basis for the determination of environmental loads for structural design. Attention shall be given to statistical description of these and other related phenomena relevant to the safe design and operation of ships and offshore structures. The committee is encouraged to cooperate with the corresponding ITTC committee.
Introduction and Metocean Forcing
Environment Committee of ISSC, by its Mandate, deals with the Metocean environments. “In offshore and coastal engineering, metocean refers to the syllabic abbreviation of meteorology and (physical) oceanography” (Wikipedia). Metocean research covers dynamics of the oceaninterface environments: the air-sea surface, atmospheric boundary layer, upper ocean, the sea bed within the wavelength proximity (~100 m for wind-generated waves), and coastal areas. Metocean disciplines broadly comprise maritime engineering, marine meteorology, wave forecast, operational oceanography, oceanic climate, sediment transport, coastal morphology, and specialised technological disciplines for in-situ and remote sensing observations. Metocean applications incorporate offshore, coastal and Arctic engineering; navigation, shipping and naval architecture; marine search and rescue; environmental instrumentation, among others. Often, both for design and operational purposes the ISSC community is interested in Metocean Extremes which include extreme conditions (such as extreme tropical or extra-tropical cyclones), extreme events (such as rogue waves) and extreme environments (such as Marginal Ice Zone, MIZ). Certain Metocean conditions appear extreme, depending on applications (e.g. swell seas are benign for recreational sailing, but can be dangerous for dredging operations and are extreme for vessels transporting liquids).
This report builds on the work of the previous Technical Committees in charge of Environment.
The goal continues to be to review scientific and technological developments in the Metocean field from the last report, and to provide context of the developments, in order to give a balanced, accurate and up to date picture about the natural environment as well as data and models which can be used to accurately simulate it. The content of this report also reflects the interests and subject areas of the Committee membership, in accordance with the ISSC I.1 mandate. The Committee has continued cooperation with the Environment Committee of ITTC and with ISSC Committee V.6 Ocean Space Utilization.
The Committee consisted of members from academia, research organizations, research laboratories and classification societies. The Committee formally met as a group in person two times before the COVID onset: in Glasgow, Scotland on the 9th of June 2019, before the 38th International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2019) and in Melbourne, Australia on the 10th of November 2019, following the 15th International Workshop on Wave Hindcasting and Forecasting. It’s also held a number of regular teleconferences: two before the face-to-face meetings and seven after, once international travel was stopped by the pandemic.
Additionally, Committee members met on an ad-hoc basis during their international travels in 2019. With the wide range of subject areas that this report must cover, and the limited space, this Committee report does not purport to be exhaustive; however, the Committee believes that the reader will be presented a fair and balanced view of the subjects covered, and we recommend this report for the consideration of the ISSC 2022 Congress.
The report consists of 11 Sections: two of which include the Introduction and Conclusions, and nine are the main content. The opening Section 1 outlines and defines Metocean Forcings which can affect the offshore design and operations and are the subject of this Review Chapter. The review of publications starts from progress in Analytical Theory in 2018-2021, Section 2. It covers the basic framework of experimental, numerical, remote sensing and all the other methods and approaches in Metocean science and engineering. Numerical Modelling (Section 3) is one of the most rapidly developing research and application environments over the past two decades, it allows us to extend the theory when analytical solutions are not possible, and to complement (or even replace) some of the experimental approaches of the past. Computer simulations will always need verification, validation and calibration of their outcomes through experiments and observations, particularly in engineering applications and offshore Metocean science. Therefore, Section 4 (Measurements and Observations) is the largest in the Chapter. Section 5 is effectively a modern extension of the measurement section – it is dedicated to Remote Sensing. Over the last four decades, the remote sensing has both become a powerful instrumental tool for field observations and remains an active area of engineering research in its own right as we see through growing developments of new capabilities in this space.
While the first five chapters are broadly dedicated to direct outcomes of Metocean research, the rest of the chapters focus more on analysis and indirect outputs. With mounting amounts of collected data: numerical, experimental, remote sensing, - Section 6 discusses advances in Data Analysis, and Section 7 in Statistics, its Theory and Analysis. Section 8, on Wave- Coupled Phenomena, reflects one of the most rapidly developing areas in Metocean science, particularly important in our era of numerical modelling. It accommodates various topics of interactions between small-scale phenomena (waves) and large-scale processes in the air-sea environments: wave breaking, wave-current and wave-ice interactions, wave influences in the Atmospheric Boundary Layer (ABL) and in the upper ocean, and complex wave-coupled modelling in the full combined air-sea-ice-wave system. Most essential for offshore engineering, is modelling and understanding of Extreme Events and Conditions, which are the subject of Section 9. Last, but not the least, Section 10 discusses Wind-Wave Climate which is connected to the global climate change. This connection is threaded throughout other sections of the chapter and is of utmost significance in offshore Metocean design and planning.

... In the joint industry project, Onboard Wave and Motion Estimator (OWME), the ocean environment was evaluated using the FFT technique, and the phases of the discretized components were optimized for the predefined wave directionalities (Dannenberg et al., 2010). By combining the wave propagation model and pre-computed response amplitude operator (RAO) model, the incident waves and the resulting ship motions were forecasted (Naaijen et al., 2016(Naaijen et al., , 2018. For the decision support system, Computer-Aided Ship Handling (CASH; Clauss et al., 2012), predictions were also performed on the wave-induced motion and hydrodynamic pressure distribution using a 3D FFT analysis. ...

This paper introduces a real-time digital twin for ship operations in seaways. The concept of the digital twin is becoming popular, and it is adopted for ship operation systems in this study. In particular, this paper introduces a new and innovative concept of the digital twin to predict ocean waves and hydrodynamic performances, such as seakeeping and maneuvering, which enables the risk and optimum route to be forecast in real time. An essential element in the realization of such a real-time digital twin is the real-time prediction of ocean waves. Hence, a sophisticated algorithm for wave reconstruction using measured wave-radar images is developed, which is extended to predicting the future evolution of a three-dimensional wave field in front of a ship within a time window of the order of 10 min. As another essential element, an analysis program to solve the coupled seakeeping-maneuvering problem is developed. This analysis can also be used in real time. By combining this with wave prediction software, the future occurrence of ocean waves and ship responses can be predicted. By extending this approach, the risk and performance of ships in various ocean environments can be predicted. In this paper, concepts, approaches, and examples are introduced.

... While sailing in the sea, the ship will be affected by wind, waves and other sea conditions, and produce a six-degree-offreedom swaying motion. These motions can lead a bad influence on the seaboard operations, like the safe navigation of the ship, the take-off and landing of carrier-based aircraft, the ship replenishment activities, etc. [1][2][3] . In that case, using the inertial measurement to measure ship motion and achieve 5 to 10 seconds of ship-motion prediction, has great significance for enhancing seaboard operational safety, improving ship motion control effects and ship combat effectiveness 4 . ...

... In the latter case, the cost-function approach relies on the approximation of the potential through lower-order formulations, impacting the physical consistency of the solution, which affects both the convergence rate of the minimization procedure and the accuracy of the predictions. Consequently, many investigations of deterministic prediction methods are performed under linear wave assumptions (e.g., [1][2][3]). Based on weakly nonlinear wave models, other studies have shown that some nonlinear properties are crucial for the correct wave field representation, especially related to the correction of the dispersion relation (e.g., [4][5][6]) which decides the velocity of the waves. ...

In view of deterministic ocean wave prediction, we introduce and investigate a new method to reconstruct ocean surfaces based on randomly distributed wave measurements. Instead of looking for the optimal parameters of a wave model through the minimization of a cost function, our approach directly solves the free surface dynamics — coupled with an interpolation operator — for the quantities of interest (i.e., surface elevation and velocity potential) at grid points that are used to compute the relevant operators. This method allows a high flexibility in terms of desired accuracy and ensures the physical consistency of the solution. Using the linear wave theory and unidirectional wave fields, we validate the applicability of the proposed method. In particular, we show that our grid-based method is able to reach similar accuracy than the wave-model parameterization method at a reasonable cost.

... Depuis quelques années, une des applications envisagées pour ces radars est l'obtention de grands jeux de données (spatio-temporelles) d'élévation de surface libre autour de leur point d'observation, qui peut être fixe ou en mouvement. De tels systèmes sont aujourd'hui proposés par Ocean-WaveS GmbH™avec WaMoS II (Hilmer et Thornhill, 2015), par NextOcean™ (Naaijen et al., 2018) ou par FutureWaves™ (Kusters et al., 2016). ...

Cette thèse présente une nouvelle méthode pour la prédiction déterministe de houle, capable de décrire précisément l'évolution d'états de mer non-linéaires tout en conservant des temps de calculs raisonnables. Une attention particulière est portée à la qualité de l'information sur la phase des vagues. Contrairement aux approches classiques qui reposent sur des mesures d'élévation de surface libre, les informations sur l'état de mer incident sont ici collectées sous la forme de profils instantanés de vitesse horizontale dus aux vagues, en amont de la zone d'intérêt. Le renseignement de cette information cinématique dans un modèle non-linéaire de propagation reposant sur une approche pseudo-spectrale permet de s'affranchir de l'étape d'assimilation de données habituellement requise dans ce genre de modèle, allégeant le temps de calcul en conservant la qualité de prédiction. Ce travail présente un diagnostic de faisabilité de cette méthode en houle unidirectionnelle. En l'absence d'instrumentation idéale pour la mesure de profils instantanés de vitesse horizontale, une méthode originale est développée pour reconstruire cette information à partir de mesures de profileurs acoustiques de courant à effet Doppler (ADCP), étendant ainsi le champ actuel d'application de ces instruments. Des études numériques de sensibilité évaluent ensuite la qualité de la prédiction obtenue pour diverses configurations de mesures et états de mers. On présente pour finir les essais en bassin conduits à Centrale Nantes, qui constituent la validation expérimentale de la méthode. Les résultats numériques et expérimentaux obtenus font de celle-ci une piste prometteuse.

... A general method to predict sea surfaces is a phase-resolved wave reconstruction via linear Thornhill, 2014, 2015;Kusters et al., 2016;Naaijen and Huijsmans, 2010;Naaijen et al., 2009Naaijen et al., , 2018Ruban, 2016;Van Groesen and Wijaya, 2017;Wijaya et al., 2015) or nonlinear models (Blondel-Couprie et al., 2013;Blondel et al., 2010;Ducrozet et al., 2016;Köllisch et al., 2018;Qi et al., 2018). Linear prediction has the advantage of computational efficiency, but it neglects wave-wave interactions and it is likely not applicable to strongly nonlinear waves. ...

Extreme waves usually emerge from intensive wave groups. Detection of wave groups from random waves may be a key step in predicting the occurrence of extreme events. A new method to discriminate wave groups in random waves based on the wavelet transform is proposed and investigated. The approach can identify wave groups effectively and efficiently. To test the methods, propagation of random wave trains over constant-spanwise submerged obstacles with a wide range of bottom slopes varying from 1:3 to 1:80 are simulated using a fully nonlinear wave model. Extreme waves satisfying the definition of freak waves are identified close to the top of the obstacles. Steeper slopes increase the probability of freak waves. Moreover, it is found that the non-dimensionalized, maximum of the scaled non-uniformity wavelet power of wave groups can be used as a precursor to predict the occurrence of extreme waves over sloping bottoms. The indicator correlates linearly with the maximum heights of wave groups. Using the simulated data, formulae to predict freak waves for various wave steepness over sloping bottoms are constructed. After testing a large number of cases, it is found that the formulae predict most extreme waves successfully and effectively.

... Due to real-time constraints, i.e., sufficient computational efficiency, existing deterministic wave prediction systems have typically used models based on linear wave theory (LWT) (Hilmer and Thornhill, 2015;Kusters et al., 2016;Naaijen et al., 2018). However, this limits their applicability to sea states with a small characteristic steepness, and further assumes that: (i) bound waves (i.e., harmonic waves that do not obey the dispersion relation) can be neglected, and (ii) the space and time scales of observations and the prediction horizon do not allow time-dependent nonlinear wave-wave interactions (e.g., nonlinear phase shift) to significantly affect wave dynamics. ...

We assess the capability of fast wave models to deterministically predict nonlinear ocean surface waves from non-uniformly distributed data such as sampled from an optical ocean sensor. Linear and weakly nonlinear prediction algorithms are applied to long-crested irregular waves based on a set of laboratory experiments and corresponding numerical simulations. An array of wave gauges is used for data acquisition, representing the typical spatial sampling an optical sensor (e.g., LIDAR) would make at grazing incidence. Predictions of the weakly nonlinear Improved Choppy Wave Model are compared to those of the Linear Wave Theory with and without a nonlinear dispersion relationship correction. Wave models are first inverted based on gauge data which provides the initial model parameters, then propagated to issue a prediction. We find that the wave prediction accuracy converges with the amount of input data used in the inversion. When waves are propagated in the models, correctly modeling the nonlinear wave phase velocity provides the main improvement in accuracy, while including nonlinear wave shape effects only improves surface elevation representation in the spatio-temporal region where input data are acquired. Surface slope prediction accuracy, however, strongly depends on the appropriate nonlinear wave shape modeling.

... Real-time phase-resolved, ocean waves can be reconstructed over some area surrounding a vessel or structure of interest by fitting a wave model to a large data set of measured surface elevations, acquired for instance with: (i) an X-band radar (Dankert & Rosenthal 2004;Nieto Borge et al. 2004;Hilmer & Thornhill 2014;Qi, Xiao & Yue 2016;Naaijen et al. 2018); or (ii) a light detection and ranging (LIDAR) camera (Belmont et al. 2007;Nouguier et al. 2014). LIDAR cameras operate in the visible light (e.g. ...

Accurate real-time simulations and forecasting of phase-revolved ocean surface waves require nonlinear effects, both geometrical and kinematic, to be accurately represented. For this purpose, wave models based on a Lagrangian steepness expansion have proved particularly efficient, as compared to those based on Eulerian expansions, as they feature higher-order nonlinearities at a reduced numerical cost. However, while they can accurately model the instantaneous nonlinear wave shape, Lagrangian models developed to date cannot accurately predict the time evolution of even simple periodic waves. Here, we propose a novel and simple method to perform a Lagrangian expansion of surface waves to second order in wave steepness, based on the dynamical system relating particle locations and the Eulerian velocity field. We show that a simple redefinition of reference particles allows us to correct the time evolution of surface waves, through a modified nonlinear dispersion relationship. The resulting expressions of free surface particle locations can then be made numerically efficient by only retaining the most significant contributions to second-order terms, i.e. Stokes drift and mean vertical level. This results in a hybrid model, referred to as the ‘improved choppy wave model’ (ICWM) (with respect to Nouguier et al. ’s J. Geophys. Res. , vol. 114, 2009, p. C09012), whose performance is numerically assessed for long-crested waves, both periodic and irregular. To do so, ICWM results are compared to those of models based on a high-order spectral method and classical second-order Lagrangian expansions. For irregular waves, two generic types of narrow- and broad-banded wave spectra are considered, for which ICWM is shown to significantly improve wave forecast accuracy as compared to other Lagrangian models; hence, ICWM is well suited to providing accurate and efficient short-term ocean wave forecast (e.g. over a few peak periods). This aspect will be the object of future work.

We develop a new methodology for the deterministic forecasting of directional ocean surface waves, based on nonlinear frequency corrections. These frequency corrections can be pre-computed based on measured energy density spectra, and therefore come at no additional computational cost compared to linear theory. The nonlinear forecasting methodology is tested on highly-nonlinear, synthetically generated seas with a variety of values of average steepness and directional spreading, and shown to consistently outperform a linear forecast.

Short-term deterministic water wave prediction is of great importance to the operations of ships and offshore structures. The use of the convolution integral of input wave profiles and an impulse response function is one of the candidates to predict water waves on the basis of the linear time-invariant system. However, this approach is not often used today because of the non-causality and the absence of the analytical solution of the impulse response function of finite-depth water; only the deep water impulse response function is available. In the paper, we present the analytical solution of the impulse response function using the dispersion relation of finite-depth water waves. In addition, the prediction abilities in space and time are investigated. It is shown that non-causal influence decreases exponentially and the predictable time increases linearly as the distance between measuring and prediction points. We conducted a tank experiment to predict irregular waves based on the JONSWAP spectrum. The prediction accuracy by the impulse response function of finite-depth water is higher than that by the deep water impulse response function. Besides, we find that the errors of the use of the analytical solution and that of the numerical solution obtained by the inverse discrete Fourier transform are comparable.

A long-standing problem in maritime operations and ocean development projects has been the prediction of instantaneous wave energy. Wave measurements collected using an array of freely drifting arrays of Surface Wave Instrument Float with Tracking (SWIFT) buoys are used to test methods for phase-resolved wave prediction in a wide range of observed sea states. Using a linear inverse model in directionally-rich, broadbanded wave fields can improve instantaneous heave predictions by an average of 63% relative to statistical forecasts based on wave spectra. Numerical simulations of a Gaussian sea, seeded with synthetic buoys, were used to supplement observations and characterize the spatiotemporal extent of reconstruction accuracy. Observations and numerical results agree well with theoretical deterministic prediction zones proposed in previous studies and suggest that the phase-resolved forecast horizon is between 1–3 average wave periods for a maximum measurement interval of 10 wave periods for ocean wave fields observed during the experiment. Prediction accuracy is dependent on the geometry and duration of the measurements and is discussed in the context of the nonlinearity and bandwidth of incident wave fields.

Model-based prediction of vessel response is valuable for planning and execution of marine operations. Response-based operation criteria are expected to give less downtime and cheaper and safer operations than criteria based on wave height and wave period. At least this holds if the response model has sufficient accuracy. The accuracy can in principle be improved by tuning the model using measured inputs and outputs. It is envisioned that an advisory system for planning and execution of marine operations will contain a module for continuous model improvement based on on-site measurements of excitation and response. A premise for this is that the measurements be of sufficiently high quality. To test the potential of automatic model tuning an established numerical vessel model is subjected to tuning with high-precision data from a model test with wave disturbance only. This may give information of how well modelling can be achieved using tuning under favourable conditions and serve as a benchmark for tuning under noisy conditions. In addition the results may give suggestions for improvement of the mathematical model. A prototype tuning software is written in Matlab. The tuning principle is to minimize the output error, i.e. the difference between measured and simulated response, by adjusting the model's parameters. For the minimization a quasi-Newton method is used. The tuning software is tested with data from the model test and found to function as intended. Examples of tuning are given.

Military sea basing operations include mooring ships together offshore and transferring cargo and equipment between them. A newly developed Environmental and Ship Motion Forecasting (ESMF) System will facilitate these operations by providing predictions of ship motions in waves. Coherent forecasts of the ship motions are provided through remote sensing of the ambient waves and using these waves as input to a predictive ship motion simulation. Key technologies developed in support of the ESMF system include: a custom-built wave sensing radar; a least squares inverse wave retrieval algorithm; a ship motion model for performing rapid seakeeping simulations; and a robust peer-to-peer system architecture. The ESMF system was tested extensively in a demonstration aboard the R/V Melville with very good results, often achieving correlations of forecast-to-realized signals of better than 80% over 30 minute intervals.
Copyright © 2015 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

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.

A series of spatial wave images recorded by a conventional marine radar is analyzed to determine the three-dimensional E(kx, ky, omega) spectrum. In the absence of a surface current the spectral energy in this three-dimensional wave number frequency space will lie on a shell defined by the dispersion relationship. Any deviation from the expected dispersion relationship can be interpreted as being due to a current induced Doppler shift of the wave frequency. A least squares curve fitting technique is used to determine the surface current required to account for the observed Doppler shift. A comparison of the radar-determined spectra and surface currents with ground truth data indicates that the radar system and analysis technique produces results consistent with conventional instrumentation.

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

The University of Michigan is leading a team that includes subcontractors Ohio State University, Aquaveo, LLC, and Woods Hole Oceanographic Institute to design, implement, and test an Environmental and Ship Motion Forecasting (ESMF) system. The system has application to many challenges associated with offshore operations, including skin-to-skin transfer of cargo/personnel and extreme wave/response prediction. Briefly, the system uses a modified commercial-off-the-shelf (COTS) Doppler marine radar to determine the wave field surrounding the vessel; nonlinear wave theory to propagate the wave surface forward in time; and seakeeping theory to predict future vessel motions. A major challenge is that all computations must be done in real time. This paper will briefly describe the system and show an example application of predicting extreme waves and motions for a floating offshore type platform.
Copyright © 2015 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