  Nonlinear instability and refraction by ocean currents are both important
mechanisms that go beyond the Rayleigh approximation and may be responsible for
the formation of freak waves. In this paper, we quantitatively study nonlinear
effects on the evolution of surface gravity waves on the ocean, to explore
systematically the effects of various input parameters on the probability of
freak wave formation. The fourth-order current-modified nonlinear Schr\"odinger
equation (CNLS4) is employed to describe the wave evolution. By solving CNLS4
numerically, we are able to obtain quantitative predictions for the wave height
distribution as a function of key environmental conditions such as average
steepness, angular spread, and frequency spread of the local sea state.
Additionally, we explore the spatial dependence of the wave height
distribution, associated with the buildup of nonlinear development.
