Beta distribution of surface elevation of random waves

A probability density function (PDF) is derived of beta distribution with b oth lambda (3) skewness) and lambda (4) (kurtosis) as parameters for weakly nonlinear wave surface elevation by use of a method recently proposed by S rokosz. This PDF not only has a simpler form than the well-known Gram-Charl ier Series PDF derived by Longuet-Higgins, but also overcomes an obvious sh ortcoming of the latter that when the series is unsuitably truncated, the r esulting PDF is locally negative. To test the derived beta PDF, laboratoria l experiments of wind waves are conducted. The experimental data indi cate that the theoretical requirements of the parameters in the beta PDF are ful filled. The experimental results show that the present PDF is in better agr eement with the measured data than the beta PDF only including parameter la mbda (3), and also than the Gram-Charlier Series PDF truncated up to the te rm of H-6.