Short Communication: Numerically simulated time to steady state is not a reliable measure of landscape response time

Abstract

Quantifying the timescales over which landscapes evolve is critical for understanding past and future environmental change. Computational landscape evolution models are one tool among many that have been used in this pursuit. We compare numerically modeled times to reach steady state for a landscape adjusting to an increase in rock uplift rate. We use three different numerical modeling libraries and explore the impact of time step, grid type, numerical method for solving the erosion equation, and metric for quantifying the time to steady state. We find that modeled time to steady state is impacted by all of these variables. Time to steady state varies inconsistently with time step length, both within a single model and among different models. In some cases, drainage rearrangement extends the time to reach steady state, but this is not consistent in all models or grid types. The two sets of experiments operating on Voronoi grids have the most consistent times to steady state when comparing across time step and metrics. On a raster grid, if we force the drainage network to remain stable, time to steady state varies much less with computational time step. In all cases we find that many measures of modeled time to steady state are longer than that predicted by an analytical equation for bedrock river response time. Our results show that the predicted time to steady state from a numerical model is, in many cases, more reflective of drainage rearrangement and numerical artifacts than the time for an uplift wave to propagate through a fixed drainage network.