Engineering applications related to the impact of sea surface waves on ships and coastal structures require detailed information about the statistical characteristics of the waves. Typically, statistical characteristics are determined on a time interval close to 20 min, which optimally meets the requirements of stationarity and statistical confidence. At the same time, it is necessary to take into account deviations from average characteristics, which can play a significant role in engineering applications (e.g. a freak wave). In this work, the wave parameters characterizing the nonlinearity were determined on time scales equal to 20, 2 and 1 min. Boundaries of changes in the skewness and excess kurtosis of sea surface elevations at different averaging scales are determined. An additional abnormality index has been introduced, equal to the ratio of the trough to the significant wave height.It is shown that the correlation coefficient between the abnormality index and excess kurtosis on the 1 and 2 min scales is higher than on the 20 min scale.