The transformation of certain parameters of an incident random wave train across the surf zone has been the subject of much study and modelling effort. In recent literature, two classes of models have been developed, which are both based on the wave energy balance or the wave action equation, but use markedly different approaches. The main goal of this study is to develop a suitable formulation for the time-varying dissipation due to wave breaking. As it is impossible to measure the time-varying dissipation directly, the formulation can only be checked by building it into models that predict measurable parameters, such as the average dissipation, the fraction of breaking waves and the mean wave energy, and by verifying these models both externally and internally. For this purpose, one wave propagation model of the probabilistic class and three models of the parametric class were formulated, calibrated and verified in this study, all based on the same dissipation formulation. Although it has not been the primary goal of the study, these models are an interesting by-product in themselves.