Directional description of ocean waves by the instantaneous direction spreading function

Directional spectrum is the most common description of ocean waves when direction is included as a parameter. However, it does not contain information on the probability distribution except for second order moments. Thus the local effects of ocean waves cannot be fully described by the directional spectrum. As an alternative description of ocean waves, the instantaneous direction spreading functions are introduced. Their interpretation and relationship with directional spectra is presented with some theoretical details. Furthermore, the instantaneous direction spreading functions can be easily estimated from pitch and roll time series, avoiding cross-spectral analysis. Some synthetic and real examples are presented.