Extreme Memory of Initial Conditions in Numerical Landscape Evolution Models

Landscape evolution models (LEMs) are dependent on their initial conditions (ICs). Commonly, LEMs use a horizontal surface with randomized perturbations as their IC and tend toward a steady state under constant forcing. The initial and steady state topographies are inherently linked, but they bear no obvious resemblance to each other. Here we reveal a connection by adding a shallow sinusoidal channel to the IC. This channel transforms into a deep canyon at steady state. Hence, the general behavior of LEMs is to indefinitely preserve topographic features from their ICs. Then we test whether experimental landscapes exhibit a similar behavior. In our experiments, we use the same sinusoidal signal, but find that it is ultimately erased. We believe that the culprit reorganizing processes are lateral channel migration and spatiotemporal variability in incision. Our results imply that LEMs are missing fundamental mechanisms and that long-term preservation of ICs in erosional environments is unlikely.