MODELING LANDSCAPE EVOLUTION WITHIN LAYERED ROCKS: WHITHER EQUILIBRIUM?

Landscape equilibrium, a long debated topic within geomorphology, underpins our interpretations of the relationships between rock type and landscape form. However, for rocks that are nearly horizontally layered, many of the common conceptions and arguments break down. Here we show why these problems arise, and explore how the conceptual framework can be generalized to examine equilibrium states within horizontally layered rocks of different erodibilities. At least two difficulties exist for the application of common conceptions of landscape equilibrium. First, as horizontal (or dipping) rocks are eroded, landscapes cannot reach topographic steady state because the spatial distribution of rock erodibility at the surface is constantly changing. Here we show that modeled landscapes in horizontal rocks instead approach a flux steady state, where the average rate of erosion and material uplift are matched at every position in the landscape when considering sufficiently long timescales. In this flux steady state, landscapes exhibit a one-to-one relationship between steepness and erodibility. However, this relationship is a function of rock dip and can be strikingly different than that predicted by topographic steady state. For example, when n<1, steeper stream channels are produced within the weaker rock layers. While this flux steady state can be described analytically, it is also a function of the full history of thicknesses and erodibilities of the exposed rock layers. This leads to the second difficulty in applying equilibrium concepts to layered rocks. The nature of flux steady state changes over time as new layers are exposed, leaving a moving target toward which the landscape is constantly evolving but never reaching. We use a combination of analytical approximations and numerical simulations to examine the dynamics of flux steady state within layered rocks and the extent to which the landscape is able to approach it, exploring the effects of different types of rock sequences and uplift histories.