A Modular Implicit Numerical Method for Hillslope Sediment Transport Laws

Abstract Long‐term hillslope evolution involves complex continuous (i.e., soil creep) and discontinuous (i.e., landslide) processes. The nonlinearity introduced using discontinuous processes poses significant challenges to the numerical stability of long‐term hillslope numerical simulations. Geomorphologists have proposed numerous sediment transport laws related to local slopes, each tailored to specific geomorphic processes. However, many complex hillslope sediment transport models, such as the depth–slope product model and the nonlinear depth‐ and slope‐dependent model, lack available implicit solution schemes. We address this issue by proposing an implicit numerical scheme named “Modular Implicit Method.” Taking the nonlinear slope‐dependent transport law as an example, our method splits the sediment transport law into gradient and coefficient functions and then directly computes the coefficient functions using a lagged strategy. Numerical experiments demonstrate that our method performs comparably to existing implicit methods in solving nonlinear transport models. Long‐term evolution simulations on realistic hillslopes show that our method enables flexible switching and co‐existence of multiple transport laws, demonstrating strong extensibility. Furthermore, the framework seamlessly couples with the stream‐power incision model, exhibiting a more general compatibility.