The difference between the joint probability distributions of apparent wave heights and periods and individual wave heights and periods

The joint distribution of wave heights and periods of individual waves is usually approximated by the joint distribution of apparent wave heights and periods.However there is difference between them.This difference is addressed and the theoretical joint distributions of apparent wave heights and periods due to Longuet-Higgins and Sun are modified to give more reasonable representations of the joint distribution of wave heights and periods of individual waves.The modification has overcome an inherent drawback of these joint PDFs that the mean wave period is infinite.A comparison is made between the modified formulae and the field data of Goda,which shows that the new formulae consist with the measurement better than their original counterparts.