Deterministic wave forecasting of nonlinear seas

Applications are invited for a three-year MPhil/PhD studentship. The studentship will start on 1 October 2021.

To apply please use the online application form. Simply search for PhD Mathematics and Statistic, then clearly state that you are applying for a PhD studentship within the School of Engineering Computing and Mathematics and name the project at the top of your personal statement.

Online application

Take a look at the Doctoral College's general information on applying for a research degree.

Project description 

Stochastic wave forecasts, which furnish averaged information about the state of the sea-surface, were introduced in the 1940s and have since reached considerable maturity. Taking atmospheric input parameters, chiefly wind, they provide information on wave heights and periods to surfers, sailors, and offshore engineers. The related problem of deterministic forecasting was long regarded as impractical – in recent years, however, with advances in remote sensing, data assimilation, and computing resources this perception has begun to change. 

The central question of deterministic wave forecasting is: if the surface elevation is known in a certain region, can one make a wave-by-wave prediction of the surface elsewhere, or at a later time? Measurements can be acquired by ship-borne radar, in-situ from wave energy devices, or from other sources. The prediction then relies on correctly capturing the dispersion and nonlinear interaction of the wave components. Moreover, given the limited forecasting horizon, a timely forecast requires a computationally simple approach that is robust under noise or measurement error. 

This project will entail a mathematical investigation of nonlinear interaction and its effects on deterministic forecasting. The forecasting methodology will be applied to realistic, directional sea-states from numerical simulations and experiments. Applications to be explored include the control of wave-energy converters, and sea-keeping for marine systems. The models developed may also serve as the starting point for physics-based machine learning systems. 

The successful candidate will join a vibrant community of maritime researchers at the University of Plymouth, encompassing mathematical and experimental approaches to understanding the sea surface.


Applicants should have (at least) a first or upper second class honours degree in mathematics, physics, engineering, or a related subject and preferably a relevant MSc or MRes qualification. 

The studentship is supported for three years and includes full home tuition fees plus a stipend of £15,609 per annum (2021/22 rate). The studentship will only fully fund those applicants who are eligible for home fees with relevant qualifications. Applicants normally required to cover international fees will have to cover the difference between the home and the international tuition fee rates (approximately £12,697 per annum).

If you wish to discuss this project further informally, please contact Dr Raphael Stuhlmeier ( However, applications must be made in accordance with the details shown below.

General information about applying for a research degree at the University of Plymouth and to apply for this position please visit:

Please mark it FAO Doctoral College and clearly state that you are applying for a PhD studentship within the School of Engineering, Computing and Mathematics.

For more information on the admissions process email the Doctoral College,

The closing date for applications is 19 April 2021. Shortlisted candidates will be invited for interview the week beginning 3 May 2021. We regret that we may not be able to respond to all applications. Applicants who have not received an offer of a place by 31 May should consider their application has been unsuccessful on this occasion.