Numerical errors in Exner equation-based bed updating for swash zone applications

Morphodynamic models rely on numerical schemes to update bed elevation in response to sediment transport gradients, a process commonly governed by the Exner equation. Despite advances in hydrodynamic and sediment transport modelling, long-term morphodynamic simulations frequently exhibit instability, spurious oscillations, or excessive diffusion, limiting their predictive reliability. These shortcomings are increasingly recognized as numerical in origin rather than purely physical. This paper presents a focused numerical analysis of Exner equation numerical schemes commonly employed in coastal morphodynamic models, with relevance to swash zone applications where feedback between evolving bed morphology and flow dynamics is strong. An analytical solution is used as a benchmark to evaluate the numerical behavior of first-order and higher-order finite difference schemes. Results demonstrate that numerical diffusion, frequency dispersion, and phase speed errors arise even under idealized conditions and accumulate rapidly with successive bed updates. The analysis shows that these numerical errors persist under the adopted idealized conditions. In fully coupled swash zone models, interactions with sediment transport and hydrodynamic feedback may alter their magnitude and development. While uncertainty in sediment flux measurement, parameterization, and boundary condition specification remains a major challenge in swash zone modelling, numerical error propagation associated with bed updating schemes represents a fundamental limitation on long-term morphodynamic prediction. By isolating and clarifying numerical error mechanisms, this study complements existing work on physical process representation and highlights the need for numerical strategies that explicitly control error accumulation in morphodynamic schemes.