Reproduction of Freak Waves Using Variational Data Assimilation and Observation

This study proposes ideas to reproduce freak waves from observational data. The reproduced data will apply to investigations on freak wave impact to offshore structures. Four-dimensional variational method (4DVAR) was used for the freak wave reproduction. Under a dynamical constraint, 4DVAR minimizes the squared error between observation and model prediction by adjusting the initial condition iteratively. This study utilizes the Higher Order Spectral Method (HOSM) to predict the nonlinear wave evolution, which is essential for freak wave generation. Information on wave spectrum estimated beforehand by a wave model is also employed to stabilize the reproduction. To increase convergence speed with fewer efforts of coding, a type of ensemble-based variational method (a4dVar) was adopted. The a4dVar performs perturbed ensemble simulations to evaluate the gradient of the squared error and is easy to parallelize and implement. This paper conducted twin experiments of HOSM+a4dVar data assimilation. HOSM model generated the true state of the uni-directional wave field, and the spatiotemporal wave field was reconstructed from time series of one virtual wave gauge located in the model. It is assumed that the virtual wave gauge detected a freak wave. The estimation accuracy of linear estimation and HOSM estimation were compared.