Shoreline evolution model from a dynamic equilibrium beach profile

• Shoreline evolution model with only 1 free-parameter.
• The model is based in a theoretical bi-parabolic EBP.
• An approximately parabolic analytical Equilibrium Energy Function (EEF) is obtained according to the theoretical EBP.
• The theoretical EBP and EEF are related to measurable beach characteristics which do not add additional free-parameters.
• The model shows no reduction of skills in comparison with state of the art models with 4 free-parameters.

Although simpler than process based models, state of the art shoreline evolution models based on the idea of cross-shore equilibrium still depend on at least 4 free-parameters. These dynamic equilibrium models are generally based on a kinetic equation in which shoreline change rate is proportional to the existing disequilibrium. Therefore a link between the model driving forces and their corresponding equilibrium shoreline position is necessary for their implementation. Until now this correlation has been established only empirically adding calibration parameters to the model.In this paper, an analytical correlation between the wave energy and the equilibrium shoreline position (“Equilibrium Energy Function”, EEF) is obtained from known invariant beach physical characteristics according to a theoretical bi-parabolic equilibrium beach profile (EBP).A wave driven shoreline evolution model related to cross-shore processes for the medium and long term is then developed with just one free-parameter as the combination of a kinetic equation simply proportional to the wave energy disequilibrium and the proposed analytical EEF.It is remarkable that, at the particular case of the beach of Nova Icaria, where the model has been calibrated and validated by means of two years of video monitoring, the proposed analytical EEF obtained only as a function of the so called EBP invariants fits shoreline observations as well as a calibrated EEF with precisely shoreline observation.The results at Nova Icaria of the proposed model show the same skills with just one calibration parameter than state of the art models with over 4 free-parameters.Nevertheless, observations in different sites with diverse beach characteristics and wave conditions are needed to widely validate the analytical form of the EEF and the shoreline evolution model proposed in this paper.