Towards modelling wave height probability distributions of "averaged" and "transient" sea states from first principles

Wind waves in seas are inherently random. Despite the progress of engineering, unpredicted extreme waves in the ocean remain a serious danger for ships and offshore structures. In recent years there was a number of accidents with large ships resulting in loss of life and pollution of large sea and coastal areas. The UK, as an island trading nation, increasingly depends on ever expanding shipping and offshore activities. The loss of life, disruption (even temporary) of supply lines or of offshore energy production have become totally (morally and economically) unacceptable. To address these challenges thorough understanding of random sea waves is needed, first of all, knowledge of the dependence of their probability distribution on wave interaction with atmosphere. In the situation of changing weather patterns the required knowledge of, say, a "100-year wave" for a particular place cannot be obtained from past experimental records, and a comprehensive theoretical model deduced from first principles is needed. Now a radical improvement compared to the present state of affairs has become possible. This is the aim of the proposed project.

At present all wave forecasting and modelling, which is a part of routine meteorological forecasting, is based on the numerical integration of the kinetic (Hasselmann) equation. The equation derived from first principles takes into account wind input, dissipation and interaction between waves of different scales and directions and describes the slow evolution of wind wave energy spectra in time and space. There has been accumulated a good understanding of spectra evolution obtained from modelling and observations. The weakest link is in translating the acquired knowledge of energy spectra into predicting probability distributions of wave heights. The major shortcomings of the prevailing approach are: (i) it relies on the very restrictive assumption of narrow spectra, while most of the observed spectra are broad from the viewpoint of nonlinear interactions, (ii) it does not properly take into account wave nonlinear interactions, (iii) it assumes stationarity of the process. Very recently PI and RCoI found a way to evaluate numerically the higher moments of probability distribution (skewness and kurtosis) within the established framework of wave turbulence without these restrictions. Since the procedure is numerically expensive, we propose to parametrize all combinations of wave spectra and thus to obtain simple parametrizations of probability distributions. This will allow us to deduce from first principles a parametrization of probability distributions easy-to-use in operational forecasting for all the variety of sea states.

The sea states predicted by the existing models or obtained as a result of direct measurements describe somehow averaged ("normal") sea states. There also exist short-lived transient states caused by sharp changes of wind, which are filtered out by such averaging. We argue that these ephemeral sea states might be responsible for disproportionate share of anomalously high waves. Such transient sea states have never been studied in this context. The time resolution of wind forecasts was far too low, there were no conceptual and numerical tools. Crucially for this project the situation has improved radically: the time resolution of wind forecasts is improving dramatically, while the PI and RCoI derived a generalized kinetic equation able to describe the fast evolution of the spectra, developed and tested the numerical code able to tackle this equation. Combining this with the authors' specially designed direct numerical simulation algorithm, we propose a clear path for examining probability distributions of wave heights of transient events linked to rapid changes of atmospheric forcing.

On this basis this project aims to revolutionise modelling of random wind waves and freak wave forecasting.

The most immediate non-academic beneficiary is ECMWF: the results of the project are to be implemented in the ECMWF routines for wave forecasting. For wave modellers there will be a new game changing set of tools for forecasting wave height probabilities:
(a) the results of heavy simulations will be parametrized in the form which will be easy to use and will be made easily available via publications;
(b) more heavy tools (original algorithms) will be also made easily available; (c) novel equation for the evolution of pdf in the wavevector space will provide, for the first time, a possibility to model and predict freak waves coming from unusual directions.

Most of the centres where model developments and wave forecasting take place are working with or within the corresponding national Meteorological Offices. ECMWF 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.

The know-how and the gains in quality of wave modelling and forecasting percolate further into a dense network of small private companies providing tailored forecasts and modelling services for different groups of end users. These companies as well as their users are also the beneficiaries.

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 expected better forecasting of waves will contribute in numerous ways to wellbeing of people in the UK and to the UK economy. 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. The outcome 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 new tools generated by the project rather than the existing ECMWF products. An earlier implementation of the results might give such companies a competitive advantage and decrease risks for everyone concerned.

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

NERC also merits a special mentioning in the list of beneficiaries: even a small decrease in the number and cost of instruments lost due to rough sea would be helpful, a better informed planning of field experiments would reduce time wasted waiting for a favourable weather window.

Now it is close to impossible to quantify the expected gains. Once implemented into operational routines our results will certainly improve the wave forecasting, but will not be able to eliminate the risks entirely. The timescale for these benefits to be realised is a few years: the results of the project have to be integrated into the operational routines by the ECMWF and then disseminated in the form of products to other centres and end users.

The RCoI will benefit from working in vibrant research atmosphere. Keele has a number of prominent scientists working on other aspects of wave dynamics. EPSAM currently has 7 Marie Curie fellows.