River flow controls on tides and tide‐mean water level profiles in a tidal freshwater river

Tidal rivers feature oscillatory and steady gradients in the water surface, controlled by interactions between river flow and tides. The river discharge attenuates the tidal motion, and tidal motion increases tidal‐mean friction in the river, which may act as a barrier to the river discharge. Time series of tidal water level amplitudes at five gauge stations along the River Mahakam in Indonesia, and tidal flow velocity amplitudes at a discharge monitoring station were obtained applying wavelet analysis. Temporal variations in tidal damping coefficients for quaterdiurnal, semidiurnal, and diurnal tidal species were quantified from the observed amplitude profiles. The analysis shows that tidal damping during the rising limb of a discharge wave differs from damping during the falling limb. Wavelet cross‐correlations between surface levels yielded empirical estimates of wave numbers. An empirical relation between tidal damping and river flow is derived to describe subtidal bottom friction along an idealized tidal river resembling the Mahakam. The subtidal friction is decomposed into contributions from the river flow only, from river‐tide interaction, and from tidal asymmetry. Even for high river flow and low tidal velocity, river flow enhances friction attributed to river‐tide interaction, causing subtidal water level setup. A simple multilinear regression model using subtidal bottom friction is employed to predict subtidal water levels at locations upstream, with a relatively good agreement between predictions and observations. The explicit expression shows the nonlinear dependence of subtidal friction on river flow velocity, explaining the complex behavior of tidal‐mean surface level profiles.