There are two popularly-used methods for wave hindcasting. One is called the singular method, another the spectral method. The latter is the method that wave conditions are given by the numerical solution of the energy balance equation. In the spectral method we need not distiguish swell from wind waves, and consider the effective fetch particularly. The former has some lacks that it's difficult to compound swell with wind waves, and deal with the effective fetch.
　The generation and growth of waves seem to be explained qualitatively by the resonance theory of Phyllips and the instability mechanism of Miles in the spectral method.
　In this paper are shown the relations of wind speeds and wave heights, the decay of waves and the decay distance etc., effectiveness of fetches and the ratio of
fetch width to length, using the nondimensional parameter, from the results for the numerical calculations for rectangular fetches. So from the results obtained
by using the spectral method, we examine the properties of waves considered in the sigular method.
　Finally we investigate the effect of the atmospheric stability etc. on the estimation of wind field, and the application of the spectral method to wave hindcasting in the field.