Spatial size of waves

•A new method to measure size of waves in spatial sea surface records is presented.•The generalized Rice’s formula is used to evaluate the probability density functions of wave sizes in a Gaussian sea.•The joint probability density of the crest height and the length of waves have been obtained through the approach.•The pdfs are given by explicit formulas but involving multidimensional Gaussian integrals.•Numerical integrations, using the methods available in MATLAB toolbox WAFO, give accurate approximations of the pdfs.

Measures of three-dimensional spatial wave size are proposed and expressed in terms of properly defined characteristics: the crest-height, the length, and the wave front location. Their statistical distributions are presented in explicit integral forms for the deep water seas modeled as Gaussian fields. The proposed approach allows for investigation of the effect that shape and directionality of the sea spectrum have on the joint distributions of the size characteristics. The method is validated by comparing numerical evaluations of the distributions with observed frequencies extracted from simulated sea surfaces. The comparisons demonstrate high accuracy of the evaluations.