  The performances of phase-averaged parametric nearshore wave transformation
models depend significantly on a reliable estimate of the wave breaker index r
(the breaker height-to-depth ratio), a free model parameter that essentially
controls the amount of breaking energy dissipation. While the previous studies
have suggested separate relationships between r and the offshore wave steepness
(s0) or the normalized local water depth (kh), the parameterization of r still
requires further investigation considering a wider variety of conditions and a
sounder physical basis. In this study, we use the field datasets of wave height
and the inverse modelling approach to reveal a composite dependence of r on
both s0 and kh. Specifically, the results show a positive dependence of r on kh
for larger s0, and a negative dependence of r on kh for smaller s0. Based on
such composite relationships, a new r formula is proposed, and its performance
is verified against the available datasets of wave height in three coasts and
14 laboratory tests. Implementation of this new formula in a parametric wave
model leads to the error reduction of wave height prediction by 10~24% (mean =
19%) relative to seven widely used models in literatures. In particular, a
remarkably higher model accuracy is obtained under wave conditions with small
offshore wave steepness, which is important for studying onshore sediment
transport and beach recovery. Two counteractive physical mechanisms for wave
nonlinearity effects, namely the breaking intensification mechanism and the
breaking resistance mechanism, are suggested to explain the opposite r-kh
relationships within different ranges of s0.
