In this book, the statistics of ocean wave phenomena is developed from the viewpoints of individual wave properties, such as height, period, and direction; climatological properties at a given time, such as significant height and directional spectra; and long term statistics of the wave climatology. Random functions, correlated in space and time, are formulated for both environmental and ocean data. Techniques, with an appropriate software library (FORTRAN and MATLAB), are provided for the analysis of data, geostatistical kriging, and the simulation of realistic artificial data. This includes a detailed development of conditional simulation (with particular emphasis on the very fast frequency domain methods), and of distribution-free empirical simulation techniques.