Back
Chapter 8

Wave modelling

CHAPTER
COORDINATORS
Lotfi Aouf and Gabriel Diaz-Hernandez
CHAPTER
AUTHORS
Alexander Babanin, Jean Bidlot, Joanna Staneva, and Andy Saulter

8.2 Wave forecast and multi-year systems

Wave forecasting consists in describing the evolution of waves under the action of wind on the ocean surface and their propagation following interactions with currents, ice, and obstacles. Wave models numerically solve the variation of the wave spectrum from the energy balance equation taking into account the energy gain and loss terms. The evolution of wave models has followed improvements in the key processes of wind-wave growth, swell dissipation, and nonlinear wave interactions. Experimental works (Mitsuyasu, 1970; Hasselmann et al., 1973) have highlighted the importance of nonlinear wave interactions and wind-wave growth. This has led to the improvement of wave models with, for example, a better simulation of the overshoot phenomenon which describes the transition of wave energy from high to low frequencies. Wave models must consider the computation time to ensure an operational forecast in near-real time conditions. So far, non-linear wave interactions have been simulated in the models in an approximate way, which sometimes generate errors.

Wave prediction is primarily a short-term process to ensure the safety of people, property, and maintenance of operational activities that require an accurate description of the sea state. In addition, wave forecasting is necessary for longterm analysis of the wave climate, to learn lessons from extreme wave events, and to upgrade and improve operational wave forecasting systems. These last actions are part of wave reanalysis or so-called multi-year products, of which the most known by users are ERA5, WAVERYS - Global Ocean Waves Reanalysis - and CFSR.

8.2.1 Architecture singularities

8.2.1.1 Levels of complexity from deep to shallow water

Every OOFS, designed to provide ocean wave-related products for both historical (multi-year) and future predictions, would require a modular architecture and a common approach methodology (see Chapter 4).

The main components of a forecasting system and of its architecture (Figure 4.1) can be considered valid for almost any OOFS architecture as they are based on three general steps:

a. Forcing and observations for data assimilation;
b. Numerical model:
c. Post-processing tools and final product information (including validation, monitoring, and dissemination).

These steps should be followed when wave OOFS is used for deep water. However, when the main process to be assessed within the OOFS are ocean waves in the coastal zone, the second step could be a major problem if not well conceptualised. The reason is that the type of numerical models to be used would not be able to obtain the results efficiently or fast enough, especially for those forecast systems that need a robust and recurrent architecture for a 24/7 output. In addition, numerical wave propagation in the coastal zone could turn rapidly into a high-CPU requirement problem, especially when singular wave physics should be solved, such as wave reflection, wave current interaction, wave overtopping over structures, etc.

Usually, wave OOFS at deep water only provides simple prediction of basic variables (called here level 1). In coastal zones, downscaling approaches were not able to obtain more complex solutions involving derived variables (called level 2 and 3), because they could not be based on direct/ trivial solutions but needed complex numerical calculations, and the use of advanced tools with high requirement of CPU time. A general list of the variables to be considered for each level (from 1 to 3) of sophistication and complexity within a wave OOFS, is shown in Figure 8.17.

8.17. Variables included in ocean wave OOFS grouped in levels from 1 to 3 depending on their complexity and codependency

The variables included will define the main architecture of the OOFS in which, through a method, effects, physical behaviour, and final prediction are linked, but allowing the possible future exchange/substitution of variables and methods in a simple and direct way.

The general architecture of modern ocean wave OOFS needs to meet certain characteristics of quality, interoperability, operation, and reliability. These characteristics should prevent anomalies that can lead to serious operational drawback such as:

  • Unrealistic results without any protocol of quality control, with solutions only found with a dynamic approach (real-time sea-state by sea-state numerical runs, as explained by Rusu et al., 2008);
  • Limited tools due to daily availability of CPU time;
  • No learning/(feedback);
  • Limited in space, geometrically inert (non-evolutionary);
  • Unknown uncertainties (no error control/measure);
  • No communication between modules, only based on a deterministic nature.

To overcome these possible shortcomings, it is then necessary to identify some architectural specificities, which are described below.

a. Efficiency and speed of predictions. The need of creating a sufficiently agile and efficient system that can provide results within the time window pre-established by the future use. Generally, this window is reduced to the very competitive time of around 1 hour, necessary to trigger all processes, obtain results, and publish them. Therefore, the general assembly method, based on a hybrid architecture combining clustering methods, should be invoked, especially for the high-CPU modelling for shallow waters.

b. Robustness (24/7). The workflow must be light and computationally ordered, to guarantee an adequate triggering of the processes and obtaining of results.

c. Modular design. This refers to the ability of the system to interchange methods and tools directly, without major modifications to the backbone architecture of the system (plug & play). This way of working requires an adequate standardisation of the intercommunication formats between modules (input and output, I/O), so that the connection of each part is compatible with the coding of the general system.

d. Reliable and realistic results. This is one of the most important characteristics for a wave OOFS as it refers to the reliability of the tool, the credibility of the general method adopted, and the satisfaction of the end user. For this purpose, there should be proposed methods for validating the tool and its results with information measured in-situ. A common practice in the development of this method is to prepare a document with instructions on how to carry out field campaigns, indicating locations, variables to be measured and type of equipment to be used, recommended schedules, suggested post-processing algorithms, and final validation products. It is important to note that the measurements will reflect the logical evolution/growth of the study area in the operational system (modification of bathymetries, evolutionary shelter elements, etc.).

e. Ad-hoc mathematical and numerical tools. This is closely related to the idea of a modular system mentioned above, and it is based on the precise integration of those tools aiming at the solution of physical processes of special interest. It is achieved through the appropriate use and adaptation of wave propagation tools (e.g. CFD models, Non-Linear Shallow Water Equations, Boussinesq-type equations, Mild Slope equations, third-generation wave generation and propagation models, etc.).

f. Self-diagnosis of results. This feature is based on the use of statistical methods that allow a detailed diagnosis of the results provided by the system on a daily basis, to identify and quantify the errors and uncertainties that are triggered throughout the execution of the system. This concept, closely linked to the "cascade of uncertainty" theory (Wilby and Dessai, 2010), makes it possible to optimise each method and reduce errors and uncertainties.

g. Nowcast integration. This refers to the capacity of the wave OOFS to take advantage of in-situ measurements provided continuously and in parallel with the use of the system during its operational phase. Algorithms should be developed for accessing, reading, post-processing, and assimilating the information measured to compare it with the predictions provided by the system, with the final capacity to generate readjustments of certain control parameters and, thus, of the predictions. This self-learning capacity of the system guarantees that, in a few months, the system will reach a mature operational level.

h. Tailor-made results. This is the OOFS’s capacity to correctly prepare the formats in which the results are presented (summary tables, email bulletins, and web pages) for the appropriate decision-making process, adapting the formats to the user needs and showing the general uncertainties in the predictions.

The architecture specificities proposed here are able to provide: i) a multi-year wave (hindcast) and b) an operational/predictive product.

8.2.1.2 Hybrid and clustering technique

A hybrid approach has been recommended (Groeneweg et al., 2006, Stansby et al., 2006) when the complexity of the physics involved in the wave propagation assessment arises conditioning: i) the numerical model (CPU time) to be used; ii) the spatial resolution of the domains to be taken into account; and iii) the temporal relevance of new variables (such as variables above level 1) to be included in the final system/solution.

This approach allows a fast assessment of variables from level 2 to 3, regardless of the sophistication of the tool that performs it. This happens thanks to the concept of "pre-executed catalogue of cases" or clustering technique (also known as pre-cooked catalogue), which is responsible for assimilating the statistics of all the casuistry of processes involved, from the forcing involved to the final response.

The hybrid method, as described in various articles (Gaslikova and Weisse, 2006; Breivik et al., 2009, Herman et al. 2009), always follows the same steps:

  • Access to the original forcing database (generally at deep water, sea-states, wind, and sea level series);
  • Apply a self-selection algorithm of N pre-selected families of cases to be run, which will cover all the physics of the climate at the outer point (Figure 8.18);
  • Transform level 1 variables to levels 2 and 3 through the execution of the N cases with the use of mainly mathematical/numerical tools;
  • Statistically reconstruct the original database (Kalra et al., 2005; Browne et al., 2007) at the transfer point after having gone through the transformation processes, e.g. from the outer harbour zone to the quay area, making use of an algorithm that statistically interrelates the pre-run catalogue of N cases with the complete statistics of the forcing in the outer zone;
  • Diagnose the data for historical diagnostic use.
Figure 8.18. Wave climate clustering using Max-Diss algorithm (source: University of Cantabria).
Previous section Next section

References

Álvarez-Fanjul, E., García-Sotillo, M., Pérez Gómez, B., García Valdecasas, J. M., Pérez Rubio, S., Rodríguez Dapena, A., et al. (2018). Operational oceanography at the service of the ports. In: “New Frontiers in Operational Oceanography”, Editors: E. Chassignet, A. Pascual, J. Tintoré, and J. Verron (Cambridge: GODAE OceanView), 729-736, https://doi.org/10.17125/gov2018.ch27

Alves, J.-H.G.M., Wittmann, P., Sestak, M., Schauer, J., Stripling, S., Bernier, N.B., Mclean, J., Chao, Y., Chawla, A., Tolman, H., Nelson, G., and Klotz, S. (2013). The NCEP–FNMOC combined wave ensemble product: expanding benefits of inter-agency probabilistic forecasts to the oceanic environment. Bulletin of the American Meteorological Society, 94(12), 1893-1905, https://doi.org/10.1175/BAMS-D-12-00032.1

Aouf, L., Hauser, D., Law-Chune, S., Chapron, B., Dalphinet, A., and Tourain, C. (2021). New directional wave observations from CFOSAT: impact on ocean/wave coupling in the Southern Ocean. EGU General Assembly 2021, online, 19-30 Apr 2021, EGU21-7412, https://doi.org/10.5194/egusphere-egu21-7412

Aouf, L., Lefèvre, J., and Hauser, D. (2006). Assimilation of Directional Wave Spectra in the Wave Model WAM: An Impact Study from Synthetic Observations in Preparation for the SWIMSAT Satellite Mission. Journal of Atmospheric and Oceanic Technology, 23(3), 448-463, https://doi.org/10.1175/JTECH1861.1

Aouf, L., Danièle, H., Céline, T., Bertrand, C. (2018). On the Assimilation of Multi-Source of Directional Wave Spectra from Sentinel-1A and 1B, and CFOSAT in the Wave Model MFWAM: Toward an Operational Use in CMEMS-MFC. IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium, 2018, pp. 5663-5666, doi:10.1109/IGARSS.2018.8517731

Ardhuin, F., Otero, M., Merrifield, S., Grouazel, A., and Terril, E. (2020). Ice breakup controls dissipation of wind waves across Southern Ocean sea ice. Geophysical Research Letters, 47, e2020GL087699. https://doi.org/10.1029/2020GL087699

Ardhuin, F., Rogers, E., Babanin, A., Filipot, J.-F., Magne, R., Roland, A., van der Westhuysen, A., Queffeulou, P., Lefevre, J.-M., Aouf, L., Collard, F. (2010). Semi-empirical dissipation source functions for ocean waves. Part I: definitions, calibration and validations. Journal of Physical Oceanography, 40, 1917-1941, https://doi.org/10.1175/2010JPO4324.1

Babanin, A.V. (2011). Breaking and Dissipation of Ocean Surface Waves. Cambridge University Press, 480 p.

Babanin, A.V. (2018). Change of regime of air-sea dynamics in extreme Metocean conditions. Proceedings of the ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering OMAE2018, June 17-22, 2018, Madrid, Spain, paper 77484, 6 p.

Babanin, A.V., Onorato, M., and Qiao, F. (2012). Surface waves and wave-coupled effects in lower atmosphere and upper ocean. Journal of Geophysical Research: Ocean, 117(C11), https://doi.org/10.1029/2012JC007932

Babanin, A.V., van der Westhuysen, A., Chalikov, D., and Rogers, W.E. (2017). Advanced wave modelling including wave-current interaction. In “The Sea: The Science of Ocean Prediction”, Eds. Nadia Pinardi, Pierre F. J. Lermusiaux, Kenneth H. Brink and Ruth Preller, Journal of Marine Research, 75, 239-262.


Barstow, S., Mørk, G., Lønseth, L., and Schjølberg, P.. (2004). Use of satellite wave data in the world waves project. Gayana (Concepción), 68(2, Supl.TIProc), 40-47, http://dx.doi.org/10.4067/S0717-65382004000200007

Battjes, J.A., and Janssen, P.A.E..M. (1978). Energy Loss and Setup Due to Breaking in Random Waves. Proceedings of 16th Coastal Engineering Conference, Hamburg, Germany, 569-587.

Bauer, E., Hasselmann, S., Hasselmann, K. and Graber, H. C. (1992). Validation and assimilation of Seasat altimeter wave heights using the WAM wave model. Journal of Geophysical Research: Ocean, C97, 12671-12682, https://doi.org/10.1029/92JC01056

Berkhoff, J. C. (1972). Computation of combined refraction-diffraction. 13th International Conference on Coastal Engineering, (pp. 471-490). ASCE.

Beven J. (2019). Hurricane Pablo tropical cyclone report, NHC-NOAA.

Bidlot J. R. (2016). Twenty-one years of wave forecast verification. ECMWF Newsletter, 150, 2016.

Booij, N., Ris, R., and Holthuijsen, Leo. (1999). A third-generation wave model for coastal regions, Part I,  Model description and validation. Journal of Geophysical Research: Ocean, 104. 7649-7656, https://doi.org/10.1029/98JC02622

Breivik, L-A., Reistad, M., Schyberg, H., Sunde, J., Krogstad, H. E., and Johnsen, H. (1998). Assimilation of ERS SAR wave spectra in an operational wave model. Journal of Geophysical Research: Ocean, 103, 7887- 7900, https://doi.org/10.1029/97JC02728

Breivik, Ø., Gusdal, Y., Furevik, B.R., Aarnes, O.J., Reistand, M. (2009). Nearshore wave forecasting and hindcasting by dynamical and statistical downscaling. Journal of Marine Systems, 78, S235-S243, https://doi.org/10.1016/j.jmarsys.2009.01.025

Breivik, Ø., Mogensen, K., Bidlot, J.-R., Balmaseda, M. A., and Janssen, P. A. E. M. (2015), Surface wave effects in the NEMO ocean model: Forced and coupled experiments. Journal of Geophysical Research: Ocean, 120, 2973-2992, https://doi.org/10.1002/2014JC010565

Brocchini, M. (2013). A reasoned overview on Boussinesq-type models: the interplay between physics,  mathematics and numerics. Proceedings of the Royal Society A Mathematical, Physics and Engineering Science, 469, https://doi.org/10.1098/rspa.2013.0496

Browne, M., Castelle, B., Strauss, D., Tomlinson, R., Blumenstein, M., Lane, C. (2007). Near-shore swell estimation from a global wind–wave model: spectral process, linear and artificial neural network models. Coastal Engineering, 54, 445-460, https://doi.org/10.1016/j.coastaleng.2006.11.007

Bunney, C., and Saulter, A. (2015). An ensemble forecast system for prediction of Atlantic-UK wind waves. Ocean Modelling, 96(1), 103-116, doi: 10.1016/j.ocemod.2015.07.005

Dean, R. G., Dalrymple, R. A. (1991). Water wave mechanics for engineers and scientists (Advanced series on ocean engineering - Volume 2), Singapore World Scientific Publishing.

Camus, P., Mendez, F., Medina, R. (2011). A hybrid efficient method to downscale wave climate to coastal areas. Coastal Engineering, 58(9), 851-862, https://doi.org/10.1016/j.coastaleng.2011.05.007

Camus, P., Mendez, F.J., Medina, R., Tomas, A., Izaguirre, C. (2013). High resolution downscaled ocean waves (DOW) reanalysis in coastal areas. Coastal Engineering, 72, 56-68, https://doi.org/10.1016/j.coastaleng.2012.09.002

Cavaleri, L., Alves, J.-H.G.M., Ardhuin, F., Babanin, A., Banner, M., Belibassakis, K., Benoit, M., Donelan, M., Groeneweg, J., Herbers, T.H.C., Hwang, P., Janssen, P.A.E.M., Janssen, T., Lavrenov, I.V., Magne, R., Monbaliu, J., Onorato, M., Polnikov, V., Resio, D., Rogers, W.E., Sheremet, A., McKee Smith, J., Tolman, H.L., van Vledder, G., Wolf, J., Young, I. (2007). Wave modeling - the state of the art. Progress in Oceanography, 75(4), 603-674, https://doi.org/10.1016/j.pocean.2007.05.005

Cavaleri, L., Abdalla, S., Benetazzo, A., Bertotti, L., Bidlot, J.-R., Breivik, Ø., Carniel, S., Jensen, R.E., Portilla-Yandun, J., Rogers, W.E., Roland, A., Sanchez-Arcilla, A., Smith, J.M., Staneva, J., Toledo, Y., van Vledder, G.Ph., and van der Westhuysen, A.J. (2018). Wave modelling in coastal and inner seas. Progress in Oceanography, 167, 164-233, https://doi.org/10.1016/j.pocean.2018.03.010

CERC, (1984). Shore Protection Manual. Department of the Army US. Army Corps of Engineers, Washington DC.

Chalikov, D. (2016). Numerical Modeling of Sea Waves. Springer, 330 p.

Chelton, D. B., and McCabe, P. J. (1985). A review of satellite altimeter measurement of sea surface wind speed: with a proposed new algorithm. Journal of Geophysical Research: Oceans, 90(3), 4707-4720, https://doi.org/10.1029/JC090iC03p04707

Chen, H.S. (2006). Ensemble Prediction of Ocean Waves at NCEP. Proceedings of 28th Ocean Engineering Conference, Taiwan.

Climate Change Initiative Coastal Sea Level Team(The).(2020). Coastal sea level anomalies andassociatedtrends from Jason satellite altimetry over 2002-2018. Scientific Data, 7, 357, https://doi.org/10.1038/s41597-020-00694-w

Dean, R. G., and Dalrymple, R. A. (1991). Water wave mechanics for engineers and scientists. In: “Advanced Series on Ocean Engineering: Volume 2” by R.G. Dean and R.A. Dalrymple, World Scientific Publishing Co Pte Ltd, https://doi.org/10.1142/1232

Derkani, M. H., Alberello, A., Nelli, F., Bennetts, L.G., Hessner, K. G., MacHutchon, K., Reichert, L., Aouf, L., Khan, S., Toffoli, A. (2021). Wind, waves, and surface currents in the Southern Ocean: observations from the Antarctic Circumnavigation Expedition. Earth System Science Data, 13, 1189-1209, https://doi.org/10.5194/essd-13-1189-2021

Dingemanns, M. (1997). Waterwave propagation over uneven bottoms. Advanced Series on Ocean Engineering, 13(2), 967.

Donelan, M., Haus, B.K., Reul, N., Plant, W., Stiassnie, M., Graber, H.C., Brown, O., Saltzman, E. (2004). On the limiting aerodynamic roughness of the ocean in very strong winds. Geophysical Research Letters, 31(18), https://doi.org/10.1029/2004GL019460

Durrant, T.H., Woodcock F., and Greenslade, D.J.M. (2009). Consensus forecasts of modelled wave parameters. Weather and Forecasting, 24, 492-503, https://doi.org/10.1175/2008WAF2222143.1

Ebert, E. (2001). Ability of a poor man’s ensemble to predict the probability and distribution of precipitation. Monthly Weather Review,129(10), 2461–2480, https://doi.org/10.1175/1520-0493(2001)129<2461:AOAPMS>2.0.CO;2

Ebert, E.E. (2008). Fuzzy verification of high resolution gridded forecasts: A review and proposed framework. Meteorological Applications, 15, 51-64, https://doi.org/10.1002/met.25

Eckart, C. (1952). The propagation of gravity waves from deep to shallow water. Circular 20, National Bureau of Standards, 165-173.

Edson, J.B., Jampana, V., Weller, R.A., Bigorre, S.P., Plueddemann, A.J., Fairall, C.W., Miller, S.D., Mahrt, L., Vickers, D., and Hersbach, H. (2013). On the exchange of momentum over the open ocean. Journal of Physical Oceanography, 43(8), 1589-1610, https://doi.org/10.1175/JPO-D-12-0173.1

Fengyan, S., Kirby, J. T., Tehranirad, B., Harris, J. C., and Grilli, S. (2012). FUNWAVE-TVD: Fully Nonlinear Boussinesq Wave Model with TVD Solver. Documentation and User’s Manual (Version 2.0). Center for Applied Coastal Research, University of Delaware, Newark, DE. Available at: https://www1.udel.edu/kirby/papers/shi-etal-cacr-11-04-version2.0.pdf

Gaslikova, L., Weisse, R. (2006). Estimating near-shore wave statistics from regional hindcasts using downscaling techniques. Ocean Dynamics, 56, 26-35, https://doi.org/10.1007/s10236-005-0041-2

Greenslade, D.J.M. and Young, I.R. (2004). Background errors in a global wave model determined from altimeter data. Journal of Geophysical Research: Oceans, 109(C9), https://doi.org/10.1029/2004JC002324

González-Marco, D., Sierra, J. P., Ybarra, O. F., Sánchez-Arcilla, A. (2008). Implications of long waves in harbour management: The Gijón port case study. Ocean & Coastal Management, 51(2), 180-201, https://doi.org/10.1016/j.ocecoaman.2007.04.001

Groeneweg, J., Ledden, M., Zijlema, M. (2007). Wave transformation in front of the Dutch Coast. Proceedings of the Coastal Engineering Conference, 552-564, https://doi.org/10.1142/9789812709554_0048

Gulev, S. K., Grigorieva, V., Sterl, A., and Woolf, D. (2003). Assessment of the reliability of wave observations from voluntary observing ships: Insights from the validation of a global wind wave climatology based on voluntary observing ship data. Journal of Geophysical Research: Oceans, 108(C7), https://doi.org/10.1029/2002JC001437

Hanley, K.E., Belcher, S.E., and Sullivan, P.P. (2010). A global climatology of wind-wave interaction. Journal of Physical Oceanography, 40, 1263-1282, https://doi.org/10.1175/2010JPO4377.1

Hanson, J. L., Phillips, O. M. (2001). Automated Analysis of Ocean Surface Directional Wave Spectra. Journal of Atmospheric and Oceanic Technology, 18(2), 277-293, https://doi.org/10.1175/1520-0426(2001)018<0277:AAOOSD>2.0.CO;2

Hansom, J. et al. (2015). Extreme Waves: Causes, Characteristics and Impact on Coastal Environments and Society January 2015. In: “Coastal and Marine Hazards, Risks, and Disasters”, Edition: Hazards and Disasters Series, Elsevier Major Reference Works, Chapter 11: Extreme Waves: Causes, Characteristics and Impact on Coastal Environments and Society. Publisher:; Elsevier; Editors: Ellis, J and Sherman, D. J.

Hasselmann, K. (1962). On the non-linear energy transfer in a gravity-wave spectrum part 1. General theory. Journal of Fluid Mechanics, 12 (4), 481-500.

Hasselmann, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K., Ewing, J. A.,Gienapp, H., Hasselmann, D. E., Kruseman, P., Meerburg, A., M¨uller, P., Olbers, D. J., Richter, K., Sell, W. and Walden, H. (1973). Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Hydraulic Engineering Reports,. Available at: https://repository.tudelft.nl/islandora/object/uuid%3Af204e188-13b9-49d8-a6dc-4fb7c20562fc

Hasselmann, K., Hasselmann, K., Bauer, E., Janssen, P., Komen, G., Bertotti, L., Lionello, P., Guillaume, A., Cardone, V., Greenwood, J., Reistad, M., Zambresky, L., Ewing, J. (1988). The WAM model - a third generation ocean wave prediction model. Journal of Physical Oceanography, 18, 1775-1810.

Hasselmann, S., Hasselmann, K., Allender, J. H., and Barnett, T. P. (1985). Computations and parameterizations of the nonlinear energy transfer in a gravity wave spectrum, II, Parameterizations of the nonlinear energy transfer for application in wave models. Journal of Physical Oceanography, 15, 1378-1391.

Hasselmann, K. (1997). Multi-pattern fingerprint method for detection and attribution of climate change. Climate Dynamics, 13, 601-611, https://doi.org/10.1007/s003820050185

Hasselmann, K., Chapron, B., Aouf, L., Ardhuin, F., Collard, F., Engen, G., Hasselmann, S., Heimbach, P., Janssen, P., Johnsen, H., et al. (2013). The ERS SAR wave mode: A breakthrough in global ocean wave observations. In: “ERS Missions: 20 Years of Observing Earth”, 1st ed.; Fletcher, K., Ed.; European Space Agency: Noordwijk, The Netherlands, 2013; pp. 165-198.

Herman, A., Kaiser, R., Niemeyer, H.D. (2009). Wind-wave variability in shallow tidal sea - spectral modelling combined with neural network methods. Coastal Engineering, 56(7), 759-772, https://doi.org/10.1016/j.coastaleng.2009.02.007

Hersbach H. (2000). Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather and Forecasting, 5(15), 1697-1709, https://doi.org/10.1175/WAF-D-16-0164.1

Hewitt, J. E, Cummings, V. J., Elis, J. I., Funnell, G., Norkko, A., Talley, T.S., Thrush, S.F. (2003). The role of waves in the colonisation of terrestrial sediments deposited in the marine environment. Journal of Experimental Marine Biology and Ecology, 290, 19-47, https://doi.org/10.1016/S0022-0981(03)00051-0

Higuera, P., Lara, L. J., Losada, I.J. (2014a). Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part I: Formulation and validation. Coastal Engineering, 83, 243-258, https://doi.org/10.1016/j.coastaleng.2013.08.010

Higuera, P., Lara, L. J., Losada, I.J. (2014b). Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part II: Application. Coastal Engineering, 83, 259-270, https://doi.org/10.1016/j.coastaleng.2013.09.002

Holthuijsen, L.H. (2007). Waves in Oceanic and Coastal Waters. Cambridge University Press, https://doi.org/10.1017/CBO9780511618536

Iafrati, A., Babanin, A.V., Onorato, M. (2013). Modulational instability, wave breaking and formation of large scale dipoles. Physical Review Letters, 110, 184504, : https://doi.org/10.1103/PhysRevLett.110.184504

Janssen, P.A.E.M (1989). Wave-induced stress and the drag of air flow over sea waves. Journal of Physical Oceanography, 19(6), 745-754, https://doi.org/10.1175/1520-0485(1989)019<0745:WISATD>2.0.CO;2

Janssen, P.A.E.M (1991). Quasi-linear theory of wind wave generation applied to wave forecasting. Journal of Physical Oceanography, 21, 1631-1642.

Janssen, P.A.E.M. (2004). The Interaction of Ocean Waves and Wind. Cambridge University Press, 308 p.

Janssen, P.A.E.M. (2012). Ocean wave effects on the daily cycle in SST. Journal of Geophysical Research: Oceans, 117, C00J32, https://doi.org/10.1029/2012JC007943

Janssen, P.A.E.M., Lionello, P., Reistad, M. and Hollingsworth, A. (1989). Hindcasts and data assimilation studies with the WAM model during the Seasat period. Journal of Geophysical Research: Oceans, C94, 973-993.

Janssen, P.A.E.M., Abdalla, S., Hersbach, H., Bidlot, J.R. (2007). Error estimation of buoy, satellite, and model wave height data. Journal of Atmospheric and Oceanic Technology, 24:1665-1677, https://doi.org/10.1175/JTECH2069.1

Kalra, R., Deo, M.C., Kumar, R., Agarwal, V.K. (2005). Artificial neural network to translate offshore satellite waves to data to coastal locations. Ocean Engineering, 32, 1917-1932, https://doi.org/10.1016/j.oceaneng.2005.01.007

Kirby, J., Dalrymple, R. (1983). Propagation of weakly nonlinear surface waves in the presence of varying depth and current. In: Proceedings of the 20th Congress, Int. Assoc. Hydraul. Res.(IAHR), Moscow, 1983, Paper S.1.5.3, pp. 198-202.

Komen, G.J., Hasselmann, K., and Hasselmann, S. (1984). On the existence of a fully developed windsea spectrum. Journal of Physical Oceanography, 14, 1271-1285.

Koutitas, C. G. (1990). Mathematical models in coastal engineering. Applied Ocean Research, 12(1), 52, https://doi.org/10.1016/S0141-1187(05)80022-7

Kudryavtsev, V.N., Makin, V.K., and Meirink, J.F. (2001). Simplified model of air flow above the waves. Boundary Layer Meteorology, 100, 63-90, https://doi.org/10.1023/A:1018914113697

Lalaurette, F. (2003). Early detection of abnormal weather conditions using a probabilistic extreme forecast index. Quarterly Journal of the Royal Meteorological Society, 129, 3037-3057, https://doi.org/10.1256/qj.02.152

Lara, J.L., Garcia, N., Losada, I.J. (2006). RANS modelling applied to random wave interaction with submerged permeable structures. Coastal Engineering, 53(5-6), 395-417, https://doi.org/10.1016/j.coastaleng.2005.11.003

Law Chune, S., Aouf, L. (2018). Wave effects in global ocean modeling: parametrizations vs. forcing from a wave model. Ocean Dynamics, 68, 1739-1758, https://doi.org/10.1007/s10236-018-1220-2

Le Traon, P.Y., Reppucci, A., Alvarez Fanjul, E., Aouf, L., Behrens, A., Belmonte, M., Bentamy, A., Bertino, L., Brando, V.E., Kreiner, M.B., Benkiran, M., Carval, T., Ciliberti, S.A., Claustre, H., Clementi, E., Coppini, G., Cossarini, G., De Alfonso Alonso-Muñoyerro, M., Delamarche, A., Dibarboure, G., Dinessen, F., Drevillon, M., Drillet, Y., Faugere, Y., Fernández, V., Fleming, A., Garcia-Hermosa, M.I., Sotillo, M.G., Garric, G., Gasparin, F., Giordan, C., Gehlen, M., Gregoire, M.L., Guinehut, S., Hamon, M., Harris, C., Hernandez, F., Hinkler, J.B., Hoyer, J., Karvonen, J., Kay, S., King, R., Lavergne, T., Lemieux-Dudon, B., Lima, L., Mao, C., Martin, M.J., Masina, S., Melet, A., Buongiorno Nardelli, B., Nolan, G., Pascual, A., Pistoia, J., Palazov, A., Piolle, J.F., Pujol, M.I., Pequignet, A.C., Peneva, E., Pérez Gómez, B., Petit de la Villeon, L., Pinardi, N., Pisano, A., Pouliquen, S., Reid, R., Remy, E., Santoleri, R., Siddorn, J., She, J., Staneva, J., Stoffelen, A., Tonani, M., Vandenbulcke, L., von Schuckmann, K., Volpe, G., Wettre, C.. and Zacharioudaki, A. (2019). From Observation to Information and Users: The Copernicus Marine Service Perspective. Frontiers in Marine Science, 6, 23, https://doi.org/10.3389/fmars.2019.00234

Lin, P. (2008). Numerical modeling of water waves (1st ed.). New York: Taylor and Francis.

Lionello, P., Gunther, H., and Janssen, P.A.E M. (1992). Assimilation of altimeter data in a global third generation wave model. Journal of Geophysical Research: Oceans, C97, 14453-14474, https://doi.org/10.1029/92JC01055

Madsen, P. A., and Larsen, J. (1987). An efficient finite-difference approach to the mild-slope equation. Coastal Engineering, 11, 329-351, https://doi.org/10.1016/0378-3839(87)90032-9

Marti F., Cazenave, A., Birol, F., Passaro, M., Léger, F., Niño, F., Almar, R., Benveniste, J., Legeais, J.F. (2021). Altimetry-based sea level trends along the coasts of Western Africa. Advances in Space Research, 68(2), 504-522, https://doi.org/10.1016/j.asr.2019.05.033

Maza, M., Lara, J. L., Losada, I. J. (2016). Solitary wave attenuation by vegetation patches. Advances in Water Resources, 98, 159-172, https://doi.org/10.1016/j.advwatres.2016.10.021

McCowan, J. (1894). On the Highest Waves of a Permanent Type. Philosophical Magazine, Edinburgh 38, 351-358.

Losada, I.J., Lara, J.L., Guanche, R., Gonzalez-Ondina, J.M. (2008). Numerical analysis of wave overtopping of rubble mound breakwaters. Coastal Engineering, 55, 47-62, https://doi.org/10.1016/j.coastaleng.2007.06.003

Mitsuyasu, H. (1970). On the growth of the spectrum of wind-generated waves. Coastal Engineering in Japan, 13(1), 1-14, https://doi.org/10.1080/05785634.1970.11924105

Mittermaier M. P., Csima, G. (2017). Ensemble versus deterministic Performance at kilometric scale. Weather and Forecasting, 32(5), https://doi.org/10.1175/WAF-D-16-0164.1

Molteni, F., Buizza, R., Palmer, T.N., Petroliagis, T. (1996). The ECMWF ensemble prediction system: methodology and validation. Quarterly Journal of the Royal Meteorological Society, 122(529), 73-119, https://doi.org/10.1002/qj.49712252905

Munk, W. H. (1950). Origin and generation of waves. Coastal Engineering Proceedings, 1, https://doi.org/10.9753/icce.v1.1

National Centers for Environmental Prediction (2012). Output fields from the NOAA WAVEWATCH III® wave model monthly hindcasts. NOAA National Centers for Environmental Information. Dataset.

Parkinson, C. L., and Cavalieri, D. J. (2012). Antarctic Sea ice variability and trends, 1979-2010. The Cryosphere, 6, 881–889, https://doi.org/10.5194/tc-6-881-2012

Pérez, B., Álvarez Fanjul, E., Pérez, S., de Alfonso, M., Vela, J. (2013). Use of tide gauge data in operational oceanography and sea level hazard warning systems, Journal of Operational Oceanography, 6(2), 1-18, https://doi.org/10.1080/1755876X.2013.11020147

Perez, J., Menendez, M., and Losada, I. J. (2017). GOW2: A global wave hindcast for coastal applications. Coastal Engineering, 124, 1-11, https://doi.org/10.1016/j.coastaleng.2017.03.005

Petroliagis, T.I., and Pinson, P. (2012). Early warnings of extreme winds using the ECMWF Extreme Forecast Index. Meteorological Applications, 21(2), 171-185, https://doi.org/10.1002/met.1339

Pezzutto P., Saulter A., Cavaleri L., Bunney, C., Marcucci, F., Sebastianelli, S. (2016). Performance comparison of meso-scale ensemble wave forecasting systems for Mediterranean Sea states. Ocean Modelling, 104, 171-186, https://doi.org/10.1016/j.ocemod.2016.06.002

Rascle N., Ardhuin, F., Queffeulou, P., Croizé-Fillon, D. (2008). A global wave parameter database for geophysical applications. Part 1: Wave-current–turbulence interaction parameters for the open ocean based on traditional parameterizations. Ocean Modelling, 25(3-4), 154-171, doi:10.1016/j.ocemod.2008.07.006

Reguero, B.G., Menéndez, M., Méndez, F.J., Mínguez, R., Losada, I.J. (2012). A global Ocean Wave (GOW) calibrated reanalysis from 1948 onwards. Coastal Engineering, 65, 38-55, https://doi.org/10.1016/j.coastaleng.2012.03.003

Ribal, A., Young, I.R. (2019). 33 years of globally calibrated wave height and wind speed data based on altimeter observations. Scientific Data, 6, 77, https://doi.org/10.1038/s41597-019-0083-9

Rusu, L., Pilar, P., Guedes Soares, C. (2008). Hindcast of the wave conditions along the west Iberian coast. Coastal Engineering, 55(11), 906-919, https://doi.org/10.1016/j.coastaleng.2008.02.029

Saetra, O., and Bidlot, J.-R. (2004). Potential benefit of using probabilistic forecasts for waves and marine winds based on the ECMWF ensemble prediction system. Weather and Forecasting, 19(4), 673-689, https://doi.org/10.1175/1520-0434(2004)019<0673:PBOUPF>2.0.CO;2

Saha, S., Moorthi, S., Pan, H.-L., Wu, X., Wang, J., Nadiga, S., … Goldberg, M. (2010). The NCEP Climate Forecast System Reanalysis. Bulletin of the American Meteorological Society, 91(8), 1015-1057, https://doi.org/10.1175/2010BAMS3001.1

Saulter A. N., Bunney, C., King, R., Water, J. (2020). An Application of NEMOVAR for Regional Wave Model Data Assimilation, Frontiers in Marine Science, 7, 579834, https://doi.org/10.3389/fmars.2020.579834

Shapiro, R. (1970). Smoothing filtering and boundary effects. Reviews of Geophysics, 8(2), 359-387, https://doi.org/10.1029/RG008i002p00359

State of the Global Climate 2020 (WMO-No. 1264).

Staneva, J., Alari, V., Breivik, Ø. et al. (2017). Effects of wave-induced forcing on a circulation model of the North Sea. Ocean Dynamics, 67, 81-101, https://doi.org/10.1007/s10236-016-1009-0

Staneva, J., Grayek, S., Behrens, A., and Günther, H. (2021). GCOAST: skill assessments of coupling wave and circulation models (NEMO-WAM). Journal of Physics: Conference Series, 1730, 012071. doi:10.1088/1742-6596/1730/1/012071

Stansby, P., Zhou, J., Kuang, C., Walkden, M., Hall, J., Dickson, M. (2007). Long-term prediction of nearshore wave climate with an application to cliff erosion. In: McKee Smith, Jane (Ed.), Proc. of International Conference Coastal Engineering, ASCE, pp. 616-627.

Stopa, J.E. (2018). Wind forcing calibration and wave hindcast comparison using multiple reanalysis and merged satellite wind datasets. Ocean Modelling, 127, 55-69, https://doi.org/10.1016/j.ocemod.2018.04.008

Swail, V., Jensen, R., Lee, B., Turton, J., Thomas, J., Gulev, S., Yelland, M., Etala, P., Meldrum, D., Birkemeier, W., Burnett, W., Warren, G. (2010). Wave Measurements, Needs and Developments for the Next Decade. Proceedings of OceanObs’09: Sustained Ocean Observations and Information for Society Conference (Volume 2), Venice, Italy, 21-25 September 2009 (J. Hall, D.E. Harrison and D. Stammer, eds.). ESA Publication WPP-306.

Thomson, J., Ackley, S., Girard-Ardhuin, F., Ardhuin, F., Babanin, A.V., Boutin, G., Brozena, J., Cheng, S., Collins, C., Doble, M., Fairall, C., Guest, P., Gebhardt, C., Gemmrich, J., Graber, H.C., Holt, B., Lehner, S., Lund, B., Meylan, M.H., Maksym, T., Montiel, F., Perrie, W., Persson, O., Rainville, L., Rogers, W.E., Shen, H., Shen, H., Squire, V., Stammerjohn, S., Stopa, J., Smith, M.M., Sutherland, P., Wadhams, P. (2018). Overview of the Arctic Sea State and Boundary Layer Physics Program. Journal of Geophysical Research: Oceans, 123(12), 8674-8687, https://doi.org/10.1002/2018JC013766

Tolman, H. L. (1989). The numerical model WAVEWATCH: a third generation model for the hindcasting of wind waves on tides in shelf seas. Communications on Hydraulic and Geotechnical Engineering, Delft Univ. of Techn., ISSN 0169-6548, Rep. no. 89-2, 72 pp.

Tolman, H.L. (2010). WAVEWATCH III development best practices. Camp Springs.

Tolman H.L., and the WAVEWATCH III® Development Group (2014). User Manual and System Documentation of WAVEWATCH III® version 4.18. Technical Note 316, NOAA/NWS/NCEP/MMAB. Available at: https://polar.ncep.noaa.gov/waves/wavewatch/manual.v4.18.pdf

Thomas, A., Mendez, F. J., and Losada, I. J. (2008). A method for spatial calibration of wave hindcast data bases. Continental Shelf Research, 28(3), 391-398, https://doi.org/10.1016/j.csr.2007.09.009

Trulsen, K. C., Nieto Borge, J., Gramstad, O., Aouf, L., and Lefèvre, J.-M. (2015). Crossing sea state and rogue wave probability during the Prestige accident. Journal of Geophysical Research: Oceans, 120, 7113-7136, https://doi.org/10.1002/2015JC011161

Tsagareli, K.N., Babanin, A.V., Walker, D.J., and Young, I.R. (2010). Numerical investigation of spectral evolution of wind waves. Part 1. Wind input source function. Journal of Physical Oceanography, 40(4), 656-666, https://doi.org/10.1175/2009JPO4370.1

Tsay, T. K., Zhu, W., and Liu, P. L.-F. (1989) A finite element model for wave refraction, diffraction, reflection and dissipation. Applied Ocean Research, 11, 33-38, https://doi.org/10.1016/0141-1187(89)90005-9

Van der Meer, J., Allsop, W., Bruce, T., Rouck, J., Kortenhaus, A., Pullen, T., Schüttrumpf, H., Troch, P., Zanuttigh, B. (2016). EurOtop: Manual on wave overtopping of sea defences and related structures - An overtopping manual largely based on European research, but for worldwide application, 2nd edition.

Van der Ven, P., Reijmerink, B., Van der Hout, A., De Jong, M. (2018). Comparison of Validation Studies of Wave - Penetration Models using Open Benchmark Datasets of Deltares, PIANC World Congress 2018, At Panama City, Panama.

Veron, F. (2015). Ocean spray. Annual Review of Fluid Mechanics, 47, 507-538, https://doi.org/10.1146/annurev-fluid-010814-014651

Visbeck, M. (2018). Ocean science research is key for a sustainable future. Nature Communication, 9, 690, https://doi.org/10.1038/s41467-018-03158-3

Voorrips, A. C., Makin V. K., and Hasselmann S. (1997). Assimilation of wave spectra from pitch-and-roll buoys in a North Sea wave model. Journal of Geophysical Research: Oceans, 102, 5829-5849, https://doi.org/10.1029/96JC03242

WAMDI group (The) (1988). The WAM Model - A Third Generation Ocean Wave Prediction Model. Journal of Physical Oceanography, 18, 1775-1810, https://doi.org/10.1175/1520-0485(1988)018<1775:TWMTGO>2.0.CO;2

Wang, J. K., Aouf, L., Dalphinet, A., Zhang, Y. G., Xu, Y., Hauser, D., Liu, J. Q. (2021). The Wide Swath Significant Wave Height: An Innovative Reconstruction of Significant Wave Heights From CFOSAT’s SWIM and Scatterometer Using Deep Learning. Geophysical Research Lettera, 48(6), https://doi.org/10.1029/2020GL091276

Wilby, R. and Dessai, S. (2010). Robust adaptation to climate change. Weather, 65, 180-185, https://doi.org/10.1002/wea.543

Young, I.R. (1999). Wind Generated Ocean Waves, Elsevier, Amsterdam, 288 p.

Zakharov, V.E. (1968). Stability of periodic waves of finite amplitude on the surface of a deep fluid. Journal of Applied Mechanics and Technical Physics, 9(2), 190-194

Zieger, S., Greenslade, D.J.M., and Kepert, J.D. (2018). Wave ensemble forecast system for tropical cyclones in the Australian region. Ocean Dynamics, 68(4-5):603-625, https://doi.org/10.1007/s10236-018-1145-9

Zijlema, M. (2009). Parallel, unstructured mesh implementation for SWAN. Proceedings of the Coastal Engineering Conference. 470-482, https://doi.org/10.1142/9789814277426_0040

Zijlema, M., Stelling, G., and Smit, P. (2011). SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters. Coastal Engineering, 58, 992-1012, https://doi.org/10.1016/j.coastaleng.2011.05.015 

Previous chapter 7
Next chapter 9
Chapter 8

Wave modelling

To start contributing, sharing knowledge and editing the WIKI, please login !