A hydrogeomorphic perspective on emergent topographic properties at landscape equilibrium

Geomorphic properties of watersheds influence runoff generation, which drives landscape evolution over long timescales. Despite this strong process feedback, our understanding of how runoff generation affects long-term catchment evolution remains rudimentary. In most humid landscapes, storm runoff arises from shallow subsurface flow and from precipitation on saturated areas. Catchment geomorphology drives these runoff mechanisms, as landscape relief generates hydraulic gradients from hillslopes to streams, and regolith thickness and permeability affect flow partitioning and water storage capacity. However, there are few studies of how runoff coupled to dynamic shallow groundwater affects landscape form. In this study, we present a new groundwater-landscape evolution model and introduce a nondimensional framework to explore how subsurface-mediated runoff generation affects long-term catchment evolution. The model solves hydraulic groundwater equations to predict the water table location given prescribed recharge. Water in excess of the subsurface capacity for transport becomes overland flow, which may detach and transport sediment, affecting the landscape form that in turn affects runoff generation. We show that (1) two input parameters fully describe the possible steady state landscapes that coevolve under steady recharge, (2) subsurface flow capacity exerts a fundamental control on hillslope length and relief of these landscapes, and (3) three topographic metrics derived from the governing equations, steepness index, Laplacian curvature, and topographic wetness index, form a natural basis for evaluating the resulting coevolved landscapes. We derive a theoretical relationship using these metrics that allows us to recover the key model input parameters (including subsurface transmissivity) from topographic analysis of the landscape. These results open possibilities for topographic analysis of humid upland landscapes that could inform quantitative understanding of hydrological processes at the landscape scale.