The propagation of the tidal wave in convergent estuaries is investigated through a one-dimensional numerical model, which allows consideration of the role of finite amplitude effects. The relevant dimensionless parameters characterizing estuarine hydrodynamics are given in terms of independent quantities, namely the geometry of the channel and the tidal forcing. Hence a suitable scale of velocity is derived, which covers both the cases of convergent and dissipative estuaries. Furthermore, the marginal conditions for tidal wave amplification, resulting from a balance between the damping effect of friction and the amplification due to channel convergence, are investigated. We show that the marginal curves can be given the form of power laws whose coefficients depend on the dimensionless tidal amplitude; the linear behavior predicted by analytical solutions is only recovered for vanishing values of the ratio between the tidal amplitude and the tidally averaged water depth. Finally, the proposed scale of velocity and that derived from the model of H. H. G. Savenije and E. J. M. Veling (2005) are tested against numerical results for a wide range of parameters.