Abstract: Currently, in the design and calculation of offshore engineering structures, the considerable low-frequency dynamic stress caused by swell is usually ignored. This simplification might potentially jeopardize the reliable operation of flexible structures, such as offshore wind turbines, for their entire lifespan. Wind-generated wave and swell are both stochastic processes that frequently occur together in the field. There exists a notable link between the statistical patterns of the two entities. In order to exploit these attributes, this study categorizes the recorded sea surface elevation data into wind-generated wave and swell components, and examines their distinct engineering properties and the interrelationship of their power spectrum density function. A novel stochastic process simulation method is introduced, which takes into account the link between aforementioned components. This paper introduces the Empirical Mode Decomposition (EMD) method as a means to effectively separate wind-generated wave and swell. This method avoids the energy vacuum problem that arises when traditional separation methods directly truncate the power spectrum of sea surface elevation. Afterwards, the power spectrum parameters of wind-generated wave and swell were identified, and a correlation matrix of these parameters was created. The results indicated a strong linear association between wind-generated wave and swell. In addition, the Copula function and regression fitting were employed to estimate the characteristics of the wind wave surge power spectrum, taking into account the correlation. Finally, the implementation of a consistent function model for wind wave surge allowed for the successful integration of synchronous simulation of the random vector process of wind wave surge through the use of the POD approach. The numerical examples demonstrate that the simulated representative samples exhibit notable wave engineering characteristics. Furthermore, the accuracy and engineering applicability of the proposed model are confirmed through various measures such as measured records, mean, standard deviation, power spectrum, and coherence function.