Unveiling the Stochasticity of Bank Erosion: A Hybrid Deterministic and Stochastic Modeling Approach

This paper presents a new hybrid deterministic‐stochastic river morphodynamics numerical modeling approach that integrates a hydrodynamic model (deterministic) with a bed morphodynamic model (deterministic) and a bank erosion model (Markovian stochastic). The hydrodynamic model solves the Shallow Water Equations and the standard ‐ model for turbulence closure. Bedload transport is estimated using the Meyer‐Peter and Müller formula, and bed evolution is solved using the Exner equation. The Markovian stochastic bank erosion model uses a new method to evaluate bank erosion risk. The approach was applied to a meander bend cutoff event in the Maiqu River on the Tibetan Plateau. Sixteen different bank‐material critical shear stress cases were considered, representing highly erodible banks ( Pa) to resistant banks ( Pa). Ten statistical realizations were performed for each case with different bank‐material erodibility to obtain ensemble‐averaged results. The flow field and bed evolution in the cutoff channel suggest that the model can successfully simulate bank erosion processes during cutoff channel evolution, and bank topographic irregularities are reasonably captured. A newly introduced calibration parameter is the ratio of mesh size to the coupling period between the bank erosion model and the hydrodynamic and morphodynamic model. Unlike the erosion rate calibration parameters used by traditional bank erosion models, the present model requires estimating the size of a typical slump failure to determine the size of the computational mesh. This new modeling approach enhanced existing tools for fluvial geomorphologists and river engineers focused on bank erosion with real‐world complex geometric features under intricate hydraulic conditions.