The development of a numerical wave prediction model incorporating a parametrical wind‐sea model and a characteristic swell model is described. The parametrical model is an extension of an earlier two‐parameter model to the full five Jonswap spectral parameters. An application is presented in which the model is used to hindcast severe wave conditions in the North Sea as part of an engineering study to define long‐term extreme wave statistics for the area. The limitations of the model and the needs for future research are discussed.

AbstractThree operational shallow water wave models are intercompared for two artificial experiments and verified for a severe storm hindcast, with the objectives of further understanding the effects of the parametrization of shallow water wave processes in numerical models.The models used are the HYPAS (Max‐Planck Institute) and GONO (KNMI) coupled‐hybrid models, and the BMO (Meteorological Office) coupled‐discrete model which are all briefly described. In the first case, depth‐dependent fetch‐limited wave growth in a steady wind is examined. In the second case a steady onshore wind is specified over an idealized constant slope coastal shelf, and the stationary wave spectra at various depths are intercompared. For the third case the wind fields for the North Sea storms of 18‐26 November 1981 were accurately reconstructed and used by each model in its operational configuration to produce a wave hindcast for this period.In case 1 the GONO and BMO models exhibit similar behaviour in the evolution of energy and peak frequency, whereas HYPAS displays less depth attenuation and little variation in peak frequency. In case 2 the energy values at different shelf depths are approximately as predicted in case 1 for HYPAS though rather higher for BMO and GONO. However, GONO and HYPAS show little change in peak frequency with depth here whereas BMO wave spectra become double‐peaked with a wind‐sea peak migrating to higher frequencies in shallower waters. In case 3, the hindcasts, all models produce qualitatively similar results. the time series of wave height and period agree well with measurements, BMO and HYPAS predicting correct energy levels except at storm peaks and GONO generally overpredicting both at lower energy levels and in a duration‐limited strong wind case. the r.m.s. error in wave height at the southern shallow water verification site is 0.5 m for all models, and varies between 0.9 m (GONO) and 1.5m (HYPAS) at the northern deep water site. Some wave spectra are presented and the directional relaxation of wind‐sea in each model is illustrated.The results of cases 1 and 2 are readily explained by the formulation of shallow water processes adopted in each model, but it is difficult to isolate and identify these mechanisms in the measured or modelied spectra from the hindcast. It is suggested that future studies involving detailed verification and intercomparison of wave models should be confined to more carefully designed wave‐measuring experiments so that less ambiguous results are obtained.

Abstract Long-term wave statistics have been generated using a deep-water numerical wave model based on a parametric method first developed from the Joint North parametric method first developed from the Joint North sea wave Project (JONSWAP). The input to the model consists of wind data from a subset of severe storms in the northern North Sea over a period 1966–1976. The wave model was compared with wave measurements at two stations. Extreme value wave statistics have been derived using the statistics from the independent storm events during the hindcast period and taking into account possible secular changes in the wind field extremes. The results are compared with wave height estimates obtained in an independent study. Introduction In engineering studies concerned with the design and certification of offshore structures it is essential to have probability estimates of the most extreme wave conditions expected during the lifetime of the structure which is typically 20 years. Reliable estimates of extreme conditions require a time base of at least 10 years from which to extrapolate to return periods of 25 years or more. Measured wave data are available at only a few stations in the northern North Sea and furthermore the data are generally intermittent or only cover a few years (see Draper). The only method available at the present time for constructing wave statistics in the area being considered has therefore to be based on a wave hindcast approach using a data base of historical wind fields. Numerical hindcast procedures are being increasingly used in sea areas where the sparse nature of wave measurements, both in time and space, make it difficult to obtain reliable design wave information. For example, in the Gulf of Mexico hurricane wave conditions have been hindcast by Patterson, and by Cardone, Pierson and Ward. Resio and Vincents have used the formulation of Barnett's wave model to derive design wave information for the Great Lakes based on carefully estimated wind fields over the past two decades. A wave hindcast study is presently being carried out by the Norwegian Meteorological Institute (Haland and Smaland) for the Norwegian continental shelf area. The purpose of this study, the North Sea wave Model (NORSWAN) project, was to generate long-term wave statistics in the North Sea and adjacent areas using hindcast wave data from severe storms occuring during the period 1966 to early 1976. The 42 storms chosen for the hindcast study were representative of all gales occurring during the period under consideration so that a representative statistical base was available for extreme value analysis. A deep water hybrid parametrical wave model (Gunther et al.) was chosen to parametrical wave model (Gunther et al.) was chosen to hindcast the wave data the wave model was checked against wave measurements at two stations near the British Isles. Finally long-term wave statistics were estimated by a storm-model approach taking into account possible changes in the wind field extremes over the last one hundred years. Details of the NORSWAM project together with the derivation of extreme value wave height estimates have been given by Ewing, Weare and Worthington. WIND FIELD SPECIFICATION A most important part of all wave hindcast studies is that concerned with the accurate specification of the wind fields over the ocean. A full description of the way the wind fields were analysed has already been given by Harding and Binding. However, as this aspect of the study is of central importance in the accuracy of the hindcast results and in the estimation of Long-term extremes, a brief description of this work will be given here. The Daily Weather Reports of the British Meteorological Office were examined for the period 1966 to early 1976 for the occurrences of gales in the northern North Sea. (Synoptic weather charts are available for periods earlier than 1966 but the data were considered too limited for the accurate reconstruction of wind fields). P. 87