The physical mechanism on the generation of the wind wave under wind forcing have been researched since around 1950 s.This phenomenon has also been researched from the probabilistic and statistical point of view,in order to aim for the application to the various problems in the ocean technology.In this paper,we are interested in the change of distribution of the sea surface level during the sea is getting stormy.It is known that the sea surface movement in the early period of the wave development under the low wind speed can be regarded to follow Gaussian process,and therefore,the marginal distribution follows Normal distribution.