Grid Resolution & The Landscape Fractal Length Scale in Channel-Hillslope Evolution, Ben Kargere ’24

Grid Resolution and The Landscape Fractal Length Scale in Channel-Hillslope Evolution, by Ben Kargere ’24, Friday April 26, 1:00 – 1:50pm, North Science Building 015, Wachenheim, Mathematics Thesis

Questions of landscape scale in coupled channel-hillslope landscape evolution have been a significant focus of geomorphological research since the 1990s. Prior work has highlighted numerous unresolved issues, particularly concerning the characteristic landscape length, the role of grid resolution, potential advection thresholds, the impact of stochastic perturbations, channel width scaling, and the dynamics of channel head locations. These elements are seemingly connected, yet their interrelationships remain unclear. In our research, we derive the landscape fractal length scale and introduce dimensionless groups to correlate it with grid resolution and boundary length. We demonstrate that the characteristic landscape length is related to the local fractal dimension on hillslopes. This connection clarifies several unresolved questions in both hillslope geomorphology and computational landscape evolution, significantly enhancing the precision of coupled landscape evolution models in replicating landscape forms, both under steady-state conditions and in response to stochastic events such as wildfires.