A practical diffusion approximation model for wave scattering by Ice Floes

The integration of advanced wave scattering physics into operational forecast systems like WAVEWATCH III is often hindered by the computational complexity of high-fidelity models. While the diffusion approximation framework of Zhao and Shen (2016) offers a promising alternative to the full Boltzmann equation, its requirement to solve for multiple coupled auxiliary variables (e.g., transmitted and scattered components) presents a significant barrier to practical implementation. To overcome this challenge, this study proposes a novel algorithmic simplification that enhances the model's computational efficiency and tractability. Our key innovation is the introduction of an effective mean action density variable, N_eff, formed by combining the transmitted energy and the isotropically redistributed scattered energy. This unification reduces the system's dimensionality, eliminating one prognostic equation and streamlining numerical integration. Validation against benchmark solutions demonstrates that the proposed model accurately captures the directional spreading of wave energy while offering a more computationally efficient pathway. By providing a streamlined and operationally viable framework, this work bridges a critical gap between theoretically rigorous scattering models and the demands of large-scale forecasting.