Extreme Memory of Initial Conditions in Numerical Landscape Evolution Models

Abstract

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.

Projections of Landscape Evolution on a 10,000 Year Timescale With Assessment and Partitioning of Uncertainty Sources

“…Comparing the drainage patterns from two model runs that differ only in the initial condition indicates that small variations in topography influence the planform shapes and positions of gullies that incise the plateaus (Figures 6a-6c). This is consistent with prior work demonstrating that drainage patterns on low-relief surfaces are sensitive to small variations in starting topography (Hancock, 2006;Ijjász-Vásquez et al, 1992;Kwang & Parker, 2019;Willgoose et al, 2003).…”

Inverting Topography for Landscape Evolution Model Process Representation: 1. Conceptualization and Sensitivity Analysis

“…We find little sensitivity to initial or boundary conditions across all models. Prior work has demonstrated sensitivity to initial condition topography when a model is initialized with a low‐relief surface decorated with random noise (Hancock, ; Hancock et al, ; Ijjász‐Vásquez et al, ; Kwang & Parker, ; Perron & Fagherazzi, ; Willgoose et al, ). But in our case study, because the postglacial topography constrains a reasonably well‐documented initial drainage pattern, such sensitivity to does not arise.…”

Offset Channels May Not Accurately Record Strike‐Slip Fault Displacement: Evidence From Landscape Evolution Models

“…Furthermore, we propose that matching thalwegs is a sufficient approach for these numerical models because the location of the thalweg is not nebulous as it may be in the natural world. In our numerical models, all flow from each pixel is routed into one pixel, so instead of building wide channels with flat bottoms and migrating thalwegs within those channel margins, channels incise deeper and become entrenched (Kwang & Parker, 2019). Thus, thalweg locations in the models do not migrate as much as they might in the real world, and the exact location of the thalweg is certain.…”