The effect of river discharge on tidal damping in estuaries is exploredwithin one consistent theoretical framework where analytical solutions areobtained by solving four implicit equations, i.e. the phase lag, thescaling, the damping and the celerity equation. In this approach the dampingequation is obtained by subtracting the envelope curves of high water and lowwater occurrence, taking into account that the flow velocity consists ofa tidal and river discharge component. Different approximations of thefriction term are considered in deriving the damping equation, resulting inas many analytical solutions. In this framework it is possible to show thatriver discharge affects tidal damping primarily through the friction term. Itappears that the residual slope, due to nonlinear friction, can have asubstantial influence on tidal wave propagation when including the effect ofriver discharge. An iterative analytical method is proposed to include thiseffect, which significantly improved model performance in the upper reachesof an estuary. The application to the Modaomen and Yangtze estuariesdemonstrates that the proposed analytical model is able to describe the maintidal dynamics with realistic roughness values in the upper part of theestuary where the ratio of river flow to tidal flow amplitude is substantial,while a model with negligible river discharge can be made to fit observationsonly with unrealistically high roughness values.
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