A geometric model for the dynamics of a fluvially dominated deltaic system under base-level change

We present a geometric model to study the role of base-level change in the dynamics of the alluvial-bedrock transition and shoreline positions in a fluvially dominated deltaic system. The domain of the problem is a sediment wedge in the long-profile cross-section. On assuming that the fluvial surface has a quadratic form, its evolution is determined by imposing an overall volume balance, and conditions for the elevations and slopes at the domain boundaries. This results in a coupled system, involving one ordinary differential equation and one non-linear equation. These equations are solved through an explicit Euler time stepping algorithm to predict the movement of the shoreline and alluvial-bedrock transition boundaries under a wide range of base-level change conditions. The mathematics of the approach are verified by comparing predictions from the geometric model with a closed form solution of a downslope gravity-driven transport model under the specific case of a square-root of time base-level change. Testing with more general base-level change scenarios reveals that this simple geometric mass balance is able to predict system dynamics that are fully consistent with both physical and numerical experiments. Moreover, model predictions under a base-level cycle (fall-rise) suggest a behavior where river incision occurs during the base-level rise stage, a predicted dynamic that has not been previously reported.