Calculation of design wave height corresponding to a return period plays an important role in coastal and ocean engineering for planning and designing of marine structures. This paper proposes a Nonlinear Least Square Method (NLSM), which estimates three unknown parameters of Weibull distribution simultaneously by an iteration method. Statistical test shows that NLSM fits each data sample very well. The effect of different parameter-fitting methods, distribution models, and threshold was also discussed in the selection of design wave heights. Best-fitting probability distribution was given and corresponding return wave heights were estimated for engineering design. Study shows that both goodness test and visual examination are prerequisite to selecting a theoretical distribution.
Calculation of design wave height corresponding to a return period plays an important role in coastal and ocean engineering for planning and designing of marine structures. The determination of the design values will greatly affects the level of protection and the scale of investment. Various studies contributed valuable findings to this topic (e.g. Petruaskas and Aagaard, 1970; Ochi, 1978; Carter and Challenor, 1981; Isaacson and MacKenzie, 1981; Muir, 1986; Goda, 1988; Vledder, et al., 1993; Goda, et al., 2000). Only one type of distribution cannot be adopted as a common extreme wave distribution because of different meteorology and geography. In order to estimate the design wave height, the most probable distribution should be selected from several candidate probabilistic models after comparison. To date, three-parameter Weibull distribution has relatively widely been used to calculate the return values. The unknown parameters of fitting distribution are mainly determined by 4 methods, namely Graphical Method (GM), Moments Method (MM), Maximum Likelihood Method (MLM), and Least Square Method (LSM). This paper proposes a Nonlinear Least Squares Method (NLSM) to fit unknown parameters of candidate distribution based on Gauss-Newton method.
