The nonlinear transformation of wave spectra in shallow water is consi
dered, in particular, the role of wave breaking and the energy transfe
r among spectral components due to triad interactions. Energy dissipat
ion due to wave breaking is formulated in a spectral form, both for en
ergy-density models and complex-amplitude models. The spectral breakin
g function distributes the total rate of random-wave energy dissipatio
n in proportion to the local spectral level, based on experimental res
ults obtained for single-peaked spectra that breaking does not appear
to alter the spectral shape significantly. The spectral breaking term
is incorporated in a set of coupled evolution equations for complex Fo
urier amplitudes, based on ideal-fluid Boussinesq equations for wave m
otion. The model is used to predict the surface elevations from given
complex Fourier amplitudes obtained from measured time records in labo
ratory experiments at the upwave boundary. The model is also used, tog
ether with the assumption of random, independent initial phases, to ca
lculate the evolution of the energy spectrum of random waves. The resu
lts show encouraging agreement with observed surface elevations as wel
l as spectra.