River Delta Formation

The prediction of the evolution of river beds and the understanding of erosion and sedimentation processes in the river delta region are very important for coastal management and the prevention of floods. While the water flow changes on the time scale of days and weeks, sedimentation and erosion in the river delta takes place on geological time scales. This large range of different time scales makes it impossible to apply classical hydrodynamical models to describe these phenomena.

We develop a model to describe the time evolution of the landscape by erosion and deposition in river beds. The model is based on a resistor network lattice where the landscape and the water height are discretized on the nodes and the flow on the bonds. The ’resistance’ of the landscape to the water flow is changed according to the water flow. If the flow is fast, the landscape is eroded and if it is slow we obtain deposition.

The novel aspects of our submitted paper lie in three fundamental points.

1. First, our reducedcomplexity model is implemented to simulate the long-term development of a real delta, the Balize Lobe of the Mississippi.
2. Second, we rescale and interpret the parameters of the model with meaningful measured physical variables in the Mississippi, such as water and sediment fluxes, the size of the delta, observed erosion and deposition rates. This step is innovative, because reduced-complexity models are not commonly adapted to real world cases, and the physical meaning of their parameters is most often left unexplored. This step also allows us to make statements about the internal consistency of the process parameterizations.
3. Third, we use the method of detrended fluctuation analysis on the modeled time series of the developing delta to illustrate the long-term memory structure which arises from the gradual deposition process and rapid change in response to channel and lobe shifting. This is a rather new analysis method in geoscience which is particularly suitable to this case, but has a wide potential in geophysical data analysis.