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Self-Organization in Fluvial Landscapes: Sediment Dynamics as an Emergent Property
DEBOER, Dirk H., (email@example.com), University of Saskatchewan, Department of Geography, 9 Campus Drive, Saskatoon, Saskatchewan, S7N 0J1, Canada
Key Words: cellular automata, emergent properties, complexity, fluvial erosion, sediment load
Landscapes are the end product of the interaction of form and process at a variety of temporal and spatial scales. As a consequence, landscapes are inherently complex. Nevertheless, at least part of the complexity of a landscape arises from processes that follow very simple rules such as: the pull of gravity results in a down slope transfer of water and sediment; a steeper slope angle results in a faster flow of water and erosion; and sediment deposition occurs when the slope angle decreases. One of the effects of these rules is that when they are applied at small scales, the resulting landscape has large-scale properties such as drainage density and drainage network configuration. These emergent properties are not part of the basic, small-scale rules but, instead, result from the application of these rules and the ensuing self-organization of the landscape.
This paper discusses a cellular model of the long-term evolution of a fluvial landscape. The model is set in motion by selecting a cell at random and applying rainfall to this cell. Erosion takes place as the water moves as runoff to the lowest neighboring cell. During the next time step, the runoff is routed from the lowest neighbour to its lowest neighbour, and in addition, a new cell to receive rainfall is selected at random. In the model, sediment is routed downslope according to a transport equation with the transport rate proportional to the slope to the power of an exponent; thus, the model allows both erosion and deposition of sediment depending on the difference between the sediment input and output of a cell. The model allows runoff from cells to converge, resulting in increased sediment transport rates downstream. Starting with a block-faulted landscape, over time a drainage network evolves. Sediment export records of the drainage basins display a complex behaviour, even though there are no external factors that would explain the variations in sediment export. The complexity of the sediment dynamics in the model arises from self-organization within the modeled system itself. Studies like these are a first step towards separating the impact of this aspect of complexity on the sediment export and depositional record from the impact of external factors associated with global change.