Modelling wind waves. What lies beyond the significant wave height?

Lead Research Organisation: Keele University
Department Name: Faculty of Natural Sciences


Modelling random wind waves in the ocean is a fundamental problem with wide ranging applications of great significance. Proper wave modelling is crucial for navigation, fisheries, offshore industries, managing of coastal environments; on the other hand, being integrated into the weather and climate models it is fundamental for air-sea interaction. Crucially, all the ocean remote sensing in various bands of electromagnetic spectrum (including the satellite, airborne, on-shore and ship based devices) relies on knowledge of wind wave field characteristics. Improving this knowledge would increase remote sensing capabilities.

Currently, all wave modelling is based on the Hasselmann kinetic equation, aka KE, and its modifications. Wind waves are random, and the KE describes evolution of ensemble averaged quantities caused by energy exchange between waves of different scales and directions owing to nonlinear resonant interactions, as well as energy input from wind and dissipation. The part concerned with the redistribution of energy between spectral components, S_nl, was considered to be firmly established for many decades, since it was derived from first principles in the same way as in other branches of physics.

The overall situation in wave modelling cannot be considered satisfactory. Although the KE does capture the behaviour of bulk characteristics (peak frequency, significant wave height) there are unexplained major systematic discrepancies between the KE modelling and the high quality observations: the observed spectra are much wider and the magnitude of the spectral peak could be considerably smaller.

The essence and main novelty of the project is in applying original direct numerical simulations algorithm (DNS-ZE) to analyse high quality data: unique observations off the Mexican coast by Romero & Melville (the Tehuantepec experiment) and data from observations by D.Hauser obtained using airborne and satellite scatterometers (KuROS and SWIM of CFOSAT). The DNS-ZE is an algorithm based on integration of a weakly nonlinear reduction of the Euler equations in nonlinear canonical variables. Currently it is the only DNS code able to perform simulations of wave evolution over several hundred kilometers. The simulations with the DNS-ZE showed excellent agreement with the observations and major discrepancies with the KE predictions.

The proposal aims to utilise the unique opportunities opened by synergy of the DNS-ZE algorithm and new high quality datasets (revisited Tehuantepec observations and processed KuROS and SWIM data) and to address the following key problems:

(i) To show that for various wave evolution scenarios supported by high quality data, the DNS-ZE indeed faithfully captures the evolution.

(ii) To retrieve the source functions (wind input and dissipation) for various steady wind conditions.

(iii) To quantify how wrong are the KE based predictions, to examine the specific implications sensitive to the shape of the spectra, e.g. for evolution of probability of freak waves, wave induced mixing in the upper ocean.

(iv) To advance in finding the cause of the KE failure.

The realisation of this project would change radically the present understanding of the accuracy of wave modelling and the serious limitations of the existing models. Advance in finding the cause of the KE failure would be a breakthrough in understanding of not only wind waves, but all kind of random nonlinear waves in fluids and plasmas.

Planned Impact

(i) The most immediate non-academic beneficiary will be ECWMF: first, the results of the project can be used for a posteriori testing of the ECWMF routines for wave forecasting. The introduction of the new metrics of assessing the outcome of modelling we are advocating (along with some other authors) can improve wave modelling. At the very least, there will be a much better understanding of what properties of wind waves can be reasonably well predicted, and what characteristics cannot be reliably captured by the existing models. For these characteristics we will provide estimates of the scale of error and its dependence on wind, fetch and other factors. For the (not uncommon) self-similar regimes of wave field evolution we will be able to provide a new tool for wave modellers - the parameterised evolution of wave spectra, higher moments of elevation and wave height probabilities. ECWMF also runs coupled models and can use our results to improve them.

(ii) Most of the centres where model developments and wave forecasting take place are working with or within the corresponding national Meteorological Offices. ECWMF distributes/shares its know-how with all EU Meteorological Offices via well established channels, hence all these centres are also direct beneficiaries of the project. We also have direct contact with the France MetOffice, where some of our finding could be tried first.

(iii) US is the second major centre of worldwide wave modelling development which pursues a philosophy different from that of the ECWMF. The NOAA/NCEP "Wavewatch" is open to experimentation; A.Babanin is a member of the team working on the next iteration of Wavewatch. We hope that we'll be able to apply some of the expected project results through this channel, which will benefit the Wavewatch users worldwide.

(iv) We expect the ocean remote sensing community also to be a major beneficiary of the project.

(v) In the longer term, the know-how and the expected gains in quality of wave modelling and forecasting percolate further into a network of small private companies providing tailored forecasts and modelling services for different groups of end users. These companies, as well as their users, will also be among the beneficiaries.

(vi) Overall, the improved ability to assess wave related risks will, first of all, help in saving lives: sea faring and off-shore activities remain dangerous, and even the largest ships and high-raised platforms are not immune to rogue waves. The better forecasting of waves will contribute in numerous ways to well-being of people in the UK and to the UK economy.

(vii) Even a minuscule reduction of risks leads to a reduction of insurance premium and thus decreases the costs of all UK import and export, which, given the scale of the UK maritime trade, becomes a significant figure. Thus it will help marine renewable developers, oil/gas offshore companies, marine services and consultancies, passenger and freight shipping companies, coastguards, fisheries, port and harbour managers. It also might give an edge to the UK maritime insurance companies, which operate globally and are one of the most competitive segments of the UK economy. In the long term the outcomes of the project will also benefit numerous UK engineering companies, which design and operate all kinds of sea related projects. More sophisticated engineering companies (like Wallingford) will also benefit from using the insights and tools generated by the project.

(viii) The realisation of the project and accumulation of theoretical expertise accompanied by publications in the top journals will enhance the UK position in the global race for investment into high end marine system engineering and all kinds of maritime activities.

(ix) The RCoI will benefit from working in vibrant research atmosphere. Keele has a number of prominent scientists and Marie Curie fellows working on other aspects of wave dynamics.


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Description Without exception the modelling wave dynamics in all wave and weather models is based on various reductions and minor modifications of the Hasselmann equation. However, there were noticeable disageements both with the results of direct numerical simulations and observations. There was no clue what might be the cause of these disageements. Nobody was looking into the nonlinear interaction term which was universally believed to be the most reliable part of the Hasselmann equation. Here, we have identified the cause of the disageements. It proved to be linked to the "closure hypotheses" which nobody questioned. It was viewed as scrosant, we showed it to be wrong. As a result of this breaktrough we have got a novel generalised kinetic equation, which is free of the shortcomings of the Hasselmann equation. This novel equation, although noticeably more complicated than the Hasselmann equation, will provide a solid foundation for wave modelling.
Exploitation Route The novel equation is too complicated to be used in operational forecasting, but it can be used (i) for better understanding of wave evolution; (ii) for better parametrizations.
Sectors Aerospace

Defence and Marine




Description ECWMF Special Projects: Role of finite non-gaussianity in the evolution of wind wave fields, with applications to freak wave prediction
Amount £10,000 (GBP)
Organisation European Centre for Medium Range Weather Forecasting ECMWF 
Sector Public
Country United Kingdom
Start 01/2022 
End 12/2024
Description Special Projects
Amount £10,000 (GBP)
Organisation European Centre for Medium Range Weather Forecasting ECMWF 
Sector Public
Country United Kingdom
Start 01/2018 
End 12/2021
Title Novel generalized kineic equation for modelling wind waves 
Description Dynamics of wind waves in all wave models, in the models of ocean-atmosphere interaction, in weather models, where waves are an important element, is simulated using various reductions of the the Hasselmann equation for random wave fields. A novel kinetic equation which addresses the fundamental shortcomings of the Hasselmann equation has been derived. The equaton captures the effects due to finite Gaussianity of wave field. It is the first model which takes into account interactions of wave correlators. 
Type Of Material Technology assay or reagent 
Year Produced 2022 
Provided To Others? Yes  
Impact At present the impact of the discovery is primarily theoretical. New approach resolves decades long contradictions. It provides the understanding of the causes of contradictions. The practical implementation of the new understanding into a numerical model is in progress. The notable tangible impacts are expected when an efficient numerical code for the model is implemented. 
Title New Generalised Kinetic Equation 
Description At present, all existing wave models are based on either the kinetic (Hassemann) equation or its reductions. It has been shown by the authors (by comparison with the DNS simmulations based upon the Zakharov equation), that modelling based upon the Hassemann) equation leads to accumulatation of very substantial (order one) errors, However, there have been alternative to the Hassemann equation. A totally novel model, the "New Generalised Kinetic Equation" (NGKE) which is free of the shortcomings of the Hassemann equation has been developed. The model takes into account finite non-gaussianity neglected in the derivation of the Hassemann equation, which results in the necessity to simulate interactions of correlators. 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? No  
Impact The devolpment has a potential to revolutionise wave modelling, although not in the short term. The new model is much more computationally costly that the currently employed models. In the short term it might be used for verification and tuning of the existing models In the long term, when vastly more abundant computational resources become available, this model will replace all existing alternatives. 
Description TAU 
Organisation Tel Aviv University
Country Israel 
Sector Academic/University 
PI Contribution We had intense discussions on how to interpret observations of short wind waves under sharply increased wind carried out in the Prof. Shemer wind wave tank. Our simulations could be used for qualitative understanding only, since we did not model the capillary effects important for the TA tank.
Collaborator Contribution Several visits of the PI were supported via Sackler Scholar Fellowship and TAU. Prof. Shemer carried experiments with instantly increasing wind which were helpful for our understanding and progress of the project. There is also a collaboration with Dr Toledo and his group on the issues concerned with the fundamentals of nonlinear wave interactions and infra-gravity waves. Dr Toledo visited Keele several times. VS visited TAU in January 2020.
Impact No immediate tangible outcomes have resulted from the collaboration with the Shemer group. Both sides have better understood limitations of the models and what is possible to observe in a relatively small facility. Collaboration with Dr Toledo resulted in a joint paper (Ocean Modelling 2017 and advance in our understanding of dynamics of infra-gravity waves in coastal waters.
Start Year 2016