Landslides and hillslope erosion increase relief

In 2018, we found exciting new results in landform evolution modeling by coupling the two simplest models of fluvial erosion and hillslope processes. While the stream-power incision model is the simplest model for detachment-limited fluvial erosion, the diffusion equation is the simplest description of hillslope processes at long timescales. Both processes were added at each grid cell without an explicit separation between channels and hillslopes because fluvial erosion automatically becomes dominant at large catchment sizes and negligible at small catchment sizes.

We found that increasing diffusion reduces the relief at small scales (individual hillslopes), but even increases the large-scale relief (entire catchments). As an immediate effect, the hillslopes become less steep. In turn, however, we observed that the network of the clearly incised valleys, which indicates dominance of fluvial erosion over diffusion, became smaller. So a smaller set of fluvially dominated grid cells had to erode the material entering from the hillslopes. To maintain a morphological equilibrium with a given uplift rate, the rivers had to steepen over long time. This steepening even overcompensated the immediate decrease in relief of the hillslopes.

This result was counterintuitive at first, but we were happy to find a reasonable explanation. So we even prepared a short manuscript for a prestigious  journal. We just did not submit it because we wanted to explain the effect quantitatively from the physical parameters of the model. From these theoretical considerations, we found that our numerical results did not only depend on the model parameters, but also on the spatial resolution of the model and noticed that this scaling problem was already discussed in a few published studies. Beyond the scaling problem, we also realized that applying the concept of detachment-limited fluvial erosion to the sediment brought from the hillslopes into the rivers is quite unrealistic. A later study including fluvial sediment transport and a model for hillslope processes that avoids scaling problems did not predict any increase in large-scale relief. So we finally realized that our original findings were mainly the result of a specific combination of models that should not be coupled this way and are not  as relevant for landform evolution as we thought.

This example illustrates many of the pitfalls of numerical modeling beyond purely technical issues. In particular, combining models that are widely used and make sense individually may still cause unexpected problems.