The actual challenge for requalification of existing offshore structures through a rational process of reassessment indicates the importance of employing a response surface methodology. At different steps in the quantitative analysis, quite a lot of approximations are performed as a surrogate for the original model in subsequent uncertainty and sensitivity studies. This paper proposes to employ a geometrical description of the nth order Stokes model in the form of a random linear combination of deterministic vectors. These vectors are obtained by rotation transformations of the wave directional vector. This facilitates introduction of an appropriate level of complexity in stochastic modeling of the wave velocity and of the Reynolds and Keulegan–Carpenter numbers for probabilistic mechanics analysis of offshore structures. In situ measurements are used to assess suitable ranges and distributions of basic variables.

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