Ultra-sensitivity of numerical landscape evolution models to their initial conditions

Numerical landscape evolution models (LEMs) are deterministic; therefore, the landscape's evolution is dependent on its initial conditions. An example of an initial condition for a LEM is the initial topography of a landscape. Commonly, the landscape is initialized as a horizontal surface with randomized perturbations. By applying a uniform and steady precipitation and base-level lowering rate, this initial topography evolves towards a steady-state landscape made up of dendritic drainage basins. The initial topography and steady-state topography are inherently linked, but they bear no resemblance to each other. Here, we reveal their connection by adding a non-randomized, Euclidian signal to our initial condition in the form of a shallow planform sinusoidal channel. This signal persists throughout the entire landscape evolution and is finally preserved indefinitely as a large valley after the landscape achieves a topographic steady-state. Hence, the general behavior of LEMs is to indefinitely embed major topological features from the initial topography into subsequent topographies. We performed a series of experiments in the eXperimental Landscape Evolution (XLE) facility at the Saint Anthony Falls Laboratory to test whether experimental landscapes exhibit a similar behavior. This facility holds a 0.5m x 0.5m x 0.3m (WxDxH) block of sediment under a precipitation generator containing multiple evenly spaced misters. Relief is created by gradually lowering a weir on one side of the sediment box. The evolution of the experimental landscape is documented by planform images and digital elevation maps with 0.5 mm resolution every 5 minutes. In our experiments, we imprint a sinusoidal channel into the initial surface and subject the landscape to a steady-uniform precipitation rate and a steady base-level lowering rate. The sinusoidal signal is erased in the transient evolutionary phase, and the network topology is completely reorganized. We believe that the culprit processes behind the reorganization are lateral channel migration and interruptions of incision in the high-order channels. Our experimental results imply that fundamental mechanisms are missing from our standard LEMs and that topological information cannot be preserved in erosional environments for prolonged periods of time.