Technical note: Common characteristics of directional spreading-steepness joint distribution in freak wave events

Abstract. Seven freak wave incidents previously documented in the real ocean in combination with model hindcast simulations are used to study the variations associated with freak wave-related parameters, such as wave steepness, directional spreading, and frequency bandwidth. Unlike the strong correlations between the freak wave parameters and freak waves' occurrence which were obtained in experimental and physical research, the correlations are not clear in the freak waves occurred in the real ocean. Wave directional spreading-steepness joint distribution is introduced and common visual features were found in the joint distribution when freak waves occur among seven "freakish" sea states. The visual features show that freak wave incidents occur when the steepness is large and directional spreading is small. Besides the steepness is large and directional spreading is small, a long-duration relatively rough sea state is also necessary for the freak wave generation. The joint distribution is more informative than the sequential variation of any single statistical wave parameter. The continuous sea states of local large steepness and small directional spreading are supposed to be "freakish" sea states, and two-dimensional distribution visualization is found to be a useful tool for freak waves forecast. The common visual features of joint distributions supply an important cue for the theoretical and experimental research.