In real systems, erosion and sedimentation rates depend on many factors such as the fluid velocity, the concentration of sediment suspended in the fluid, the vegetation in the channel walls, and the material into which the channel is formed. In addition, changes in channel capacity over time would likely be influenced by human activity such as repair works. Our model simplifies this very complex set of conditions to focus on the primary role of fluid velocity in channel erosion and sedimentation. It is worth noting here that our model considers the topology fixed to a specific set of edges and nodes and therefore cannot account for effects such as flood waters breaching the banks of channels or the erosion of new channels. The dynamics can change the weights (capacities) associated with each edge but cannot cause the formation of new edges in the current implementation.

In addition to the assumption of fixed topology, we assume only that fluid flow is conserved and that channel capacity (cross-sectional area) increases from erosion or decreases from sedimentation at a rate that is proportional to both the flow through the channel, and the degree to which the fluid velocity is above or below a predefined threshold for erosion or sedimentation, respectively. After specifying the control parameters and initializing the network to its equilibrium state, the flood flows were added to the supersource and to each of the edges. Then, the flow was distributed through the network, and new edge capacities were calculated from the increased flow velocities. The damage to the network was then computed by distributing the equilibrium flow through the damaged network and calculating Q. The simulation ended if Q converged to a specified degree. If not, the simulation incremented forward (tt′), and the process repeated with the new edge capacities. Here, we identified convergence asEmbedded Image(1)

During the cascade, erosion and sedimentation dynamics were not applied to edges between the supersource and real source nodes, as these represent disparate regions of the watershed. These edges maintain the same flood flows throughout the simulation.

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