wave-attenuation-1d: An idealized one-dimensional framework for wave attenuation through coastal vegetation using Numba-accelerated shallow water equations

Sandy Hardian Susanto Herho , Iwan Pramesti Anwar, Theo Raynold Evontianus Buala Nama Ndruru, Rusmawan Suwarman, Dasapta Erwin Irawan

Coastal vegetation provides crucial wave attenuation for shoreline protection, yet existing models are either computationally prohibitive or lack transparency for educational purposes. This study presents wave-attenuation-1d, an open-source Python package implementing linearized shallow water equations with vegetation-induced drag to simulate wave propagation through coastal vegetation. The governing equations are derived from first principles through systematic application of shallow water assumptions, depth-integration, and linearization, yielding coupled continuity and momentum equations where vegetation effects enter as a dissipative drag term proportional to velocity. The numerical implementation employs fourth-order Runge-Kutta time integration with implicit treatment of drag terms on a staggered grid, achieving unconditional stability for stiff dissipative terms. Numerical experiments with monochromatic waves propagating through a 40-meter vegetation patch demonstrate transmission coefficients ranging from 0.799 for sparse vegetation to 0.011 for dense vegetation, corresponding to wave height reductions of 20.1% and 98.9%, respectively. While the one-dimensional framework necessarily simplifies three-dimensional flow structures, turbulence generation, and flexible vegetation dynamics, the model provides a transparent, computationally efficient baseline for understanding fundamental wave-vegetation interactions. The package features standardized NetCDF output with CF-compliant metadata, and modular architecture that facilitates both educational applications and extensions toward more sophisticated models. This work bridges the gap between research-grade simulations and accessible tools for coastal engineering education, providing a foundation for exploring nature-based solutions for coastal protection.