The legacy of initial conditions in landscape evolution

Landscapes subject to constant forcing tend to evolve toward equilibrium states in which individual landforms have similar characteristics. Yet, even in landscapes at or near equilibrium, there can be significant variability among individual landforms. Furthermore, sites subject to similar processes and conditions can have different mean landform characteristics. This variability is often ascribed to on-going transient evolution, or to heterogeneity in processes, material properties, forcing, or boundary conditions. Three surprising outcomes of landform evolution models suggest, however, that such variability could arise in equilibrium landscapes without any heterogeneity in the physical processes shaping the topography. First, homogeneous systems subjected to constant forcing can generate a heterogeneous distribution of equilibrium landforms. Second, even simple non-linear systems can have multiple stable equilibrium states. Third, evolving landscapes can exhibit path dependence and hysteresis. We show how these three mechanisms can produce variability in landforms that arises from the characteristics of the initial topographic surface rather than from heterogeneity in geomorphic processes. Numerical experiments on the formation of low-order fluvial valleys and transportational cyclic steps in erodible streambeds illustrate why it is important to consider the influence of initial conditions when comparing models with natural topography, estimating the uncertainty of model predictions, and studying how landscapes respond to disturbances. Copyright © 2011 John Wiley & Sons, Ltd.