to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Wave climate analysis for the design of wave energy harvesters in the Mediterranean Sea

This paper presents a literature survey on time-dependent statistical modelling of extreme waves and sea states. The focus is twofold: on statistical modelling of extreme waves and space- and time-dependent statistical modelling. The first part will consist of a literature review of statistical modelling of extreme waves and wave parameters, most notably on the modelling of extreme significant wave height. The second part will focus on statistical modelling of time- and space-dependent variables in a more general sense, and will focus on the methodology and models used also in other relevant application areas. It was found that limited effort has been put on developing statistical models for waves incorporating spatial and long-term temporal variability and it is suggested that model improvements could be achieved by adopting approaches from other application areas. In particular, Bayesian hierarchical space–time models were identified as promising tools for spatio-temporal modelling of extreme waves. Finally, a review of projections of future extreme wave climate is presented.

/pdf/long-term-time-dependent-stochastic-modelling-of-extreme-43emmxwtnz.pdf

Long-term time-dependent stochastic modelling of extreme waves

This study develops a stochastic approach to model short-crested stormy seas as random fields both in space and time. Defining a space–time extreme as the largest surface displacement over a given sea surface area during a storm, associated statistical properties are derived by means of the theory of Euler characteristics of random excursion sets in combination with the Equivalent Power Storm model. As a result, an analytical solution for the return period of space–time extremes is given. Subsequently, the relative validity of the new model and its predictions are explored by analyzing wave data retrieved from NOAA buoy 42003, located in the eastern part of the Gulf of Mexico, offshore Naples, Florida. The results indicate that, as the storm area increases under short-crested wave conditions, space–time extremes noticeably exceed the significant wave height of the most probable sea state in which they likely occur and that they also do not violate Stokes–Miche-type upper limits on wave heights.

Space–Time Extremes in Short-Crested Storm Seas

This paper concerns the crest height statistics arising in sea states that are broad banded in both frequency and direction. A new set of laboratory observations are presented and the results compared with the commonly applied statistical distributions. Taken as a whole, the data confirm that the crest-height distributions are critically dependent upon the directionality of the sea state. Although nonlinear effects arising at third order and above are most pronounced in uni-directional seas, the present data show that they are also important in directionally spread seas, provided the seas are sufficiently steep and not too short crested. The data also highlight the limiting effects of wave breaking. With individual breaking events dependent upon the local wave steepness, the directionality of the sea state again plays a significant role. Indeed, the present observations confirm that the two competing processes of nonlinear amplification and wave breaking can have a profound influence on the crest-height distributions leading to significant departures from established theory. In such cases, the key parameters are the sea state steepness and directional spread; the latter acting to counter the former in terms of nonlinear changes in the crest-height distributions.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2012.0696

A laboratory study of wave crest statistics and the role of directional spreading

[1] This paper deals with the long-term statistics for extreme nonlinear crest heights. First, a new analytical solution for the return period R(η), of a sea storm in which the maximum nonlinear crest height exceeds a fixed threshold η, is obtained by applying the ‘Equivalent Triangular Storm’ model and a second-order crest height distribution. The probability P(ηc max > η∣[0, L]) that maximum nonlinear crest height in the time span L exceeds a fixed threshold is then derived from R(η) solution, assuming that the occurrence of storms with highest crest larger than η is given by a Poisson process. In the applications, both R(η) and P(ηc max > η∣[0, L]) are calculated for some locations. It is shown that narrowband second-order approach is slightly conservative, with respect to the more general condition of crest distribution for second-order three-dimensional waves. Finally, a comparison with Boccotti, Jasper and Krogstad models is presented.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2005JC003407

Return period of nonlinear high wave crests

A generalized approach for long-term modelling of extreme crest-to-trough wave heights

Three-dimensional nonlinear random wave groups in intermediate water depth

In this paper some statistical properties of random waves in a sea storm are investigated. The classical Borgman’s approach is applied to obtain the analytical expressions of both the probability PK (H) that in a sea storm only K waves higher than a fixed threshold H occur, and the probability P≥K (H) that in a sea storm at least K waves higher than a fixed threshold H occur, with K = 1, 2, 3,[[ellipsis]] Moreover, it is shown that, if the number K is negligible in comparison with the number of waves occurring in the storm, the results may be expressed in an integral form. This integral form is very useful to particularize both PK (H) and P≥K (H) for a storm with a triangular time history. Finally, the results are validated with Montecarlo simulations of random waves in a sea storm of given time history.Copyright © 2006 by ASME

Some Statistical Properties of Random Waves in a Sea Storm

The paper proposes the directional analysis of the severest storms recorded by the Italian Wave Measurement Network (RON) For this purpose the buoy data have been processed and all the storms have been selected; for the strongest storms, the direction of the sea states, which form them, has been analyzed The directional return period of sea storms in which the maximum significant wave height exceeds a threshold is then obtained, by applying the ETS model It is found that, for the prediction of extreme storms off Italy, it is possible to assume the duration of storms constant, with an error smaller than 4%Copyright © 2006 by ASME

Diego Pavone

Papers

Return period of nonlinear high wave crests

A generalized approach for long-term modelling of extreme crest-to-trough wave heights

Three-dimensional nonlinear random wave groups in intermediate water depth

Some Statistical Properties of Random Waves in a Sea Storm

Directional Return Period of Severe Storms Off Italian Coasts