Optimized Variational 1D Boussinesq modelling of coastal waves propagating over a slope

► An Optimized Variational Boussinesq Model (OVBM) is designed for waves above uneven bottom. ► The kinetic energy functional is used for the choice of optimal vertical profiles. ► Simulations with a finite element implementation of the OVBM agree very well with experimental data of bichromatic and irregular waves.