Stationarity of mean erosion rate but topography still moving (beginners)

For beginners.

At the end of simulations, it can be seen that a nearly steady-state has been reached: the maximum elevation does not change so much. If you plot the mean denudation rate or mean elevation from the file provided in the downloadable zip (below each simulation movie) you will see that both have reached a constant value at the end. This state is defined as the dynamic equilibrium, namely the state where the tectonic uplift is balanced by the erosion at mountain scale. Yet, the topography is still moving and the steady-state is not perfect. Some catchments are growing, others are decreasing. This behaviour seems related with the multiple flow algorithm used in Cidre (water and sediment are spread towards all the downstream cells and not only the cell in the steepest direction). This does not appear with steepest-descent algorithm. Experts can read Pelletier (2004). Such a behaviour has been observed in experiments of catchment erosion (Hasbargen and Paola2000). Methods to detect growing and reducing catchments have been invented recently (Willett et al.2014) and could be applied on simulated topographies. The important point is that drainage network can evolve even during dynamic equilibrium in absence of any climatic or tectonic variations.

References

   Hasbargen, L. E., and C. Paola (2000), Landscape instability in an experimental drainage basin, Geology, 28, 1067–1070.

   Pelletier, J. D. (2004), Persistent drainage migration in a numerical landscape evolution model, Geophys. Res. Lett., 31, L20,501, doi:10.1029/2004GL020802.

   Willett, S. D., S. W. McCoy, J. T. Perron, L. Goren, and C.-Y. Chen (2014), Dynamic Reorganization of River Basins, Science, 343(6175), 1117+, doi:10.1126/science.1248765.

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