The safety and effectiveness of offshore and marine operations can be greatly enhanced by combining real-time measurements of the wave field surrounding a vessel with short-term forecasts of the sea state. The objectives of this Ph.D. research project are to develop an efficient numerical model to predict nonlinear evolution of multi-directional sea states, and a technique to assimilate real time radar data into the model efficiently in order to provide improved forecasts of the short term evolution of the sea surface.

The wave prediction model is based on a pair of coupled nonlinear evolution equations for the free surface elevation and tangential velocity on the free surface. These equations are solved numerically using a pseudo-spectral method in which both variables are approximated by a truncated Fourier series. All linear operations in the evolution equations are evaluated in Fourier space while the nonlinear operations are computed in physical space and the fourth order Runge-Kutta scheme is used to evolve the variables in time. The numerical model is validated with the exact solutions for one and two-dimensional steady and free waves and experimental data for modulation instability.

Radar returns are inherently mixed with noise while numerical models suffer from the lack of correct initial conditions and discretization errors. Therefore, an efficient assimilation scheme is developed to find the optimal initial conditions that best fit a series of observations over a finite time interval. This is done by minimizing a cost function which is defined as the difference between measured and numerically predicted values of surface elevation. The gradient of the cost function with respect to the initial conditions is calculated using the adjoint technique. The data assimilation scheme is validated using synthetically generated observations for two and three-dimensional flows as well as real radar data collected from field experiments conducted off a ship in Alaska in April 2006.