[1] Analytical solutions of the one-dimensional hydrodynamic equations for tidal wave propagation are now available and, in this paper, presented in explicit equations. For given topography, friction, and tidal amplitude at the downstream boundary, the velocity amplitude, the wave celerity, the tidal damping, and the phase lag can be computed. The solution is based on the full nonlinearized St. Venant equations applied to an exponentially converging channel, which may have a bottom slope. Two families of solutions exist. The first family consists of mixed tidal waves, which have a phase lag between zero and p/2, which occur in alluvial coastal plain estuaries with almost no bottom slope; the second family consists of ''apparent standing'' waves, which develop in short estuaries with a steep topography. Asymptotic solutions are presented for progressive waves, frictionless waves, waves in channels with constant cross section, and waves in ideal estuaries where there is no damping or amplification. The analytical method is accurate in the downstream, marine part of estuaries and particularly useful in combination with ecological or salt intrusion models. The solutions are compared with observations in the Schelde, Elbe, and Mekong estuaries.

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