Measurements of fetch-limited wave spectra from various sources indicate an approximate invariance of the normalized spectral shape with fetch. It has been suggested from investigations of the spectral energy balance that this can be explained by the shape-stabilizing influence of nonlinear resonant wave-wave interactions, which are also responsible for the migration of the spectral peak to lower frequencies. Analyses of a series of further data sets obtained under non-uniform, non-stationary wind conditions show that the invariance of the spectral shape is not restricted to uniform-wind, fetch-limited situations, but applies generally for a growing wind sea. The observed shape invariance is exploited in a wave prediction model by projecting the full transport equation for the two-dimensional spectral continuum onto two variables characterizing the energy and frequency scales of the spectrum. Inspection of the resultant equations reveals further simplifications, enabling the system to be reduced ... Abstract Measurements of fetch-limited wave spectra from various sources indicate an approximate invariance of the normalized spectral shape with fetch. It has been suggested from investigations of the spectral energy balance that this can be explained by the shape-stabilizing influence of nonlinear resonant wave-wave interactions, which are also responsible for the migration of the spectral peak to lower frequencies. Analyses of a series of further data sets obtained under non-uniform, non-stationary wind conditions show that the invariance of the spectral shape is not restricted to uniform-wind, fetch-limited situations, but applies generally for a growing wind sea. The observed shape invariance is exploited in a wave prediction model by projecting the full transport equation for the two-dimensional spectral continuum onto two variables characterizing the energy and frequency scales of the spectrum. Inspection of the resultant equations reveals further simplifications, enabling the system to be reduced ...