|Title||On the extension of the freak wave warning system and its verification|
|Year of Publication||2009|
|Authors||Janssen, PAEM, Bidlot, J-R|
|Secondary Title||Technical Memorandum|
|Type of Work||Technical Memorandum|
This memo discusses a number of updates to the freak wave warning system which were introduced in cycle 33R1 of the IFS. The list of changes is given below and they are discussed in more detail in the remainder of this memo. They are: 1. In shallow water it is well-known that for kD ≃ 1.363 the effects of four-wave interactions vanish because of the generation of a wave-induced current. Following the work of Janssen and Onorato (2007), a parametrization of this shallow water effect is introduced which affects both the time evolution of the wave spectrum, and the determination of the kurtosis of the wave field. 2. Extension of the ECMWF freak wave warning system to two-dimensional propagation. Numerical simulations and experimental evidence suggest that the kurtosis of the surface elevation then depends on two parameters, namely the Benjamin-Feir Index (BFI) and a parameter which measures the importance of directional width compared to the width of the frequency spectrum. 3. Introduction of two extreme wave parameters, namely the average maximum wave height and the corresponding wave period. Following the work of Mori and Janssen (2006) it is suggested to use the maximum wave height, observed during a period of length T as an indicator of how extreme the sea state is. For known probability distribution of the sea surface elevation it is shown how to obtain an estimate of the average maximum wave height. A fairly extensive validation of products of the freak wave warning system is also presented, in particular regarding the maximum wave height. A comparison of the expected maximum wave height against buoy observations shows a good agreement, while also the theoretical probability distribution function of maximum wave height matches the observed distribution very well, in particular in the extremes.