The adaptive multiscale moment method (AMMM) was originally developed to solve Fredholm equation. More recently, this method has demonstrated to be effective for scattering problems. In this article, we show that AMMM is a relevant approach to model and to analyze the electromagnetic scattering by coastal breaking sea waves. The shape of breaking wave results from very nonlinear fluid mechanics and is a complex target for electromagnetic scattering. This article presents an efficient hydrodynamic model and, combined with AMMM, a global realistic numerical simulation of the electromagnetic signature induced by breaking sea waves.