Skewness and Kurtosis of the Surface Wave in the Coastal Zone of the Black Sea

Abstract

Purpose. The aim of the study is to analyze variability of the statistical moments characterizing deviations of the sea surface elevation distributions from the Gaussian. Methods and Results. Field studies of the sea waves’ characteristics were carried out from the stationary oceanographic platform located in the Black Sea near the Southern coast of Crimea. The data obtained both in summer and winter, were used. The statistical moments were calculated separately for wind waves and swell. The measurements were performed in a wide range of meteorological conditions and wave parameters (wind speed varied from 0 to 26 m/s, wave age – from 0 to 5.2 and steepness – from 0.005 to 0.095). For wind waves, the coefficients of skewness correlation with the waves’ steepness and age were equal to 0.46 and 0.38. The kurtosis correlation coefficients with these parameters were small (0.09 and 0.07), but with the confidence level 99.8% – significant. For swell, the correlation coefficients were 1.5 – 2.0 times lower. Conclusions. The statistical moments of the sea surface elevations of the third and higher orders are the indicators of the wave field nonlinearity, which should be taken into account when solving a wide range of the applied and fundamental problems. The deviations of the surface elevation distributions from the Gaussian one are not described unambiguously by the steepness and wave age. At the fixed values of these parameters, a large scatter in the skewness and kurtosis of the surface elevations is observed. This imposes significant limitations on the possibility of applying the nonlinear wave models based on the wave profile expansion by small parameter (steepness) degrees, in engineering calculations.

Statistical modeling of the sea surface in the presence of abnormal waves

“…4 and 1 approximately correspond to their limit values observed in the coastal zone of the Black Sea[25,26].…”

“…Let's compare the model and calculated from the measurement data of the probability density functions of sea surface elevations. To do this, we will use the data of direct wave measurements obtained on the stationary oceanographic platform of the Marine Hydrophysical Institute of the RAS [25]. The data of continuous measurements were divided into sessions lasting 20 minutes, for each of which the values of skewness and excess kurtosis were calculated, according to which the model was built  …”

Simulation of sea surface elevations by the Edgeworth distribution

“…In these situations, the values 4  exceed 4 [16,17], the values 3  may be lower than -0.3 [18]. Measurements carried out in the field and laboratory conditions showed that 3  and 4  are not correlated with each other [19,20].…”

“…There are practically no data on changes in the fifth statistical moment. Therefore, for further analysis, we will use regression, which connects Regression (10) is based on the data of direct wave measurements carried out on a stationary oceanographic platform [20]. The platform is installed in the coastal zone of the Black Sea near the southern coast of Crimea.…”

Ka-Band Doppler Scatterometry: A Strong Wind Case Study

“…Sea currents were measured by a propeller current meter installed at 10 m depth. Wave measurements were performed by conductive wire wave gauges, mounted at the vertices of a triangle with 5.31 m, 11.63 m, and 15.48 m sides [39]. Two-dimensional (2-D) directional frequency spectra were estimated using a standard approach, with north-south and east-west wave slopes calculated from instantaneous triangle inclinations and wave elevations taken from one of the wires [40,41].…”