In this chapter the probabilistic modelling of hull girder primary loading and response are presented. In the first part the probabilistic modelling of the sea environment is described. The nature of the sea surface is described in qualitative terms, following which the short-term description is presented. Deterministic modelling is discussed and statistics descriptors of ocean wave records defined. The concept of the wave spectrum is introduced and spectra for moderate and rough sea states described and differentiated, as well as wave spectra for ship design. Ship response to wave loading is discussed. The importance of linear response is underlined and structural considerations described. The basis of extreme value theory is presented and the Fisher-Tippett-Gnedenko theorem is introduced. Extreme as well as combined loads in short-term seas are described. Long-term analysis of sea loads is considered next. Differences with short-term analysis are mentioned and the use of full-scale measurements at sea described. The statistical description of a critical wave height is described using firstly the return period, and probability of occurrence method and secondly the wave height and period approach (scatter diagram). Two methods used to conduct long-term analysis of sea states are described: the long-term cumulative distribution (LTCD) method and the simulation method.

The concepts of sea state and of short-term and long-term statistics are introduced. Wave by wave and spectral analyses are described; definitions are given of wave spectrum, significant wave height, mean wave period, and narrowness parameter. Theoretical distributions of wave heights (the Rayleigh law) are derived. The concept of return period is introduced. The other environmental parameters considered are the wind, the current, the internal waves, and the marine growth. The different definitions of mean wind velocity are explained. Typical wind profiles and wind spectra are presented.