The data of long-term surface wave measurements by bottom pressure sensors near Sakhalin Island are used to analyze statistical characteristics of the coastal waves, and to build instrumental probability distributions for exceedance of wave heights. Specific features of the observations conducted during the periods of open and ice-covered sea surfaces are discussed. To construct a subset of statistically homogeneous samples, data sorting by natural physical dimensionless parameters (dimensionless depth, wave steepness, shallow water nonlinear parameter, Ursell parameter) is proposed. With the help of this approach, the effects of nonlinearity and water depth on probability distributions are estimated with a focus on abnormally high waves.
The measurements of surface waves with bottom pressure sensors have been performed in the coastal zone of the Sea of Okhotsk near Sakhalin Island by the Special design office of an automation equipment of sea researches since 2009. These data have been used to evaluate the statistical characteristics of surface waves with particular interest to abnormally high waves (so-called "rogue waves" (Kharif C. et al, 2009). The bank of accumulated measurement data off Sakhalin Island already contains several thousand records of very high waves that satisfy the formal criterion of exceeding the significant wave height Hs by 2 times or more, with the amplification index AI = H/Hs > 2 (Zaytsev et al., 2011; Kuznetsov et al., 2014; Kokorina et al., 2022).
For linear waves with narrowband spectrum the exceedance probability of normalized wave heights H/Hs is described with the Rayleigh distribution (Massel, 1996):
(Equation)
The significant wave height could be defined as the mean of one third of the highest waves in the record, Hs = H1/3 or through the RMS surface displacement σ, Hs = 4σ. In what follows we use Hs when the particular definition is not important, and 4σ and H1/3 otherwise. The Rayleigh distribution (Eq. 1) is commonly used as a first approximation to estimate the likelihood of rogue wave formation: PR(H = 2Hs) ≈ 3.35⋅10–4. According to this estimate, the actual probability of rogue waves approximately corresponds to the following value: on average, 2–3 abnormal waves per day, what is more or less confirmed in the previous analysis of measurements in the concerned area (Kuznetsov et al., 2014). A more accurate assessment of the probability of rare extreme events H > 2Hs and the search for conditions that lead to an increase in the probability of such events are topical problems of modern oceanography.