The energy transfer equation, which describes the evolution of the surface wave spectrum, is solved numerically for different water depths, with an empirical expression for the bottom dissipation and explicit calculations of the resonant four-wave interactions. The resulting growth curves for total energy, peak frequency, etc., are explained from the balance between the source terms at the various stages of growth. The equilibrium which is reached between bottom friction and the resonant interactions on the forward face of the spectrum turns out to be important. The calculated results are briefly compared with recent shallow water wave experiments (TMA, Lake Marken) and with the Coastal Engineering Research Centre growth curves. Finally the results are compared with the SWIM study. ¿ American Geophysical Union 1988