The Simulation

In the bachelor's thesis "Development of Mountain Ranges and their Rivers - A Cellular Automaton Simulation" an erosion model of mountain ranges was developed. The model works as a two dimensional cellular automaton and includes the geomorphological surface processes of fluvial erosion, toppling and landslides. Key-aspect of the simulation was the implementation of a fluvial network, leading to a coupling of the different processes to the development of the underlying network.

Precipitation to the landscape is drained through the fluvial network, following the path of steepest descent at every cell. This causes - supposed time integrated - erosion and long-distance sediment transport by water run-off and is considered with fluvial erosion. In the developing landscape landslides and toppling - differing mainly in the size of their failure plane - are stochastically triggered according to the relation of slope height to a maximum stable height.

Main Results

The introduction of a fluvial network and thereby the separation of the time scale of water flow and erosion, as well as the reduction to surface processes in a two-dimensional landscape projection, reduced computational effort significantly. Furthermore fluvial networks are known to show self-organized behaviour [e.g. Maritan et al., "Scaling laws for river networks", 1996 in Phys. Rev. E]. Figure 1 shows the characteristic power-law-like decreasing in number of cells with increasing drainage area. Here the total number of cells greater or equal to a certain drainage area were counted. However, this also led to a strong coupling of local slope and water drainage. Figure 2 shows their functional dependency in a system of constant uplift of the landscape with fluvial erosion as only process.

  • Figure 1: Self-organisation of the fluvial network. The frequency of exceedance in drainage area reduces power-law-like with increasing drainage area.
  • Figure 2: Functional relation of the slopes to the fluvial drainage area, forced by steady tectonic uplift and fluvial river incision.

The fluvial network was found to be a very stable system and the stochastic processes of landslides and toppling had only small influence on global structures. Acting more like diffusive processes, both processes of material failure had influence on the smaller scale shape and interfered with the process of fluvial erosional. The movement of sediments by material failure caused a shift of high fluvial erosion rates away from hilltops and toward the valleys. The additional sediments in the valley overwhelmed transport capacities of the streams and changed the valley topography (figure 3).

  • a) without toppling
  • b) with toppling - low influence,
    due to steep maximum slope and low frequency
  • c) with toppling - medium influence,
    due to low maximum slope and low frequency
  • d) with toppling - high influence,
    due to low maximum slope and high frequency

Figure 3: Influence of toppling on mountain range shape for the same flat initialisation and even uplift. Toppling smoothed the previously rough ridges and was slowing the effective erosion progressively. It counteracted the incision of streams into bedrock.