  An extensive data set of water level measurements of the September 2015
Chilean tsunami in rivers in Japan and a new methodology for data processing
are used to verify that tsunami dissipation in a river at each instant and
locality depends on the tidally-modified wave-locked slope of the river
surface. As deduced from the observations, a relatively small tsunami or ocean
noise traveling at mild wave-locked slopes can propagate virtually without
losses to the upstream locations where observed tidal ranges are a fraction of
that downstream; though at the higher slopes, tidal and riverine currents
combined efficiently damp the shorter waves. The observed correlations between
the tsunami admittance upriver and the traveled wave-locked slopes are
explained analytically under the fully-nonlinear shallow-water approximation.
It is found that the wave-locked slope in a purely incident wave relates to the
bottom drag in the same manner as a steady surface slope does for a stationary
flow. For a small-amplitude tsunami in the study rivers, the wave-locked slope
in a co-propagating tidal wave defines the background current and thereby
friction experienced by the tsunami.
