A document by David G Litwin. Click on the document to view its contents.

Features of landscape morphology—including slope, curvature, and drainage dissection—are important controls on runoff generation in upland landscapes. Over long timescales, runoff plays an essential role in shaping these same features through surface erosion. This feedback between erosion and runoff generation suggests that modeling long-term landscape evolution together with dynamic runoff generation could provide insight into hydrological function. Here we examine the emergence of variable source area runoff generation in a new coupled hydro-geomorphic model that accounts for water balance partitioning between surface flow, subsurface flow, and evapotranspiration as landscapes evolve over millions of years. We derive a minimal set of dimensionless numbers that provide insight into how hydrologic and geomorphic parameters together affect landscapes. We find an inverse relationship between the dimensionless local relief and the fraction of the landscape that produces saturation excess overland flow, in agreement with the synthesis described in the “Dunne Diagram.’ Furthermore, we find an inverse, nonlinear relationship between the Hillslope number, which describes topographic relief relative to aquifer thickness, and the proportion of the landscape that variably saturated. Certain parameter combinations produce features with wide valley bottom wetlands and nondendritic, diamond-shaped drainage networks, which cannot be produced by simple landscape evolution models alone. With these results, we demonstrate the power of coupled hydrogeomorphic models for generating new insights into hydrological processes, and also suggest that subsurface hydrology may be integral for modeling aspects of long-term landscape evolution.

The hydrologic dynamics and geomorphic evolution of watersheds are intimately coupled – runoff generation and water storage are controlled by topography and properties of the surface and subsurface, while also affecting the evolution of those properties over geologic time. However, the large disparity between their timescales has made it difficult to examine interdependent controls on emergent hydro-geomorphic properties, such as hillslope length, drainage density, extent of surface saturation. In this study, we develop a new model coupling hydrology and landscape evolution to explore how runoff generation affects long-term catchment evolution, and analyze numerical results using a nondimensional scaling framework. We focus on hydrologic processes dominating in humid climates where storm runoff primarily arises from shallow subsurface flow and from precipitation on saturated areas. The model solves hydraulic groundwater equations to predict the water table location given prescribed, constant groundwater recharge. Water in excess of the subsurface capacity for transport becomes overland flow, which generates shear stress on the surface and may detach and transport sediment. This affects the landscape form that in turn affects runoff generation. We show that (1) three dimensionless parameters describe the possible steady state landscapes that coevolve under steady recharge; (2) hillslope length increases with increasing transmissivity relative to the recharge rate; (3) three topographic metrics—steepness index, Laplacian curvature, and topographic index—provide a basis to recover key model parameters from topography (including subsurface transmissivity). These results open possibilities for topographic analysis of humid upland landscapes that could inform quantitative understanding of hydrological processes at the landscape scale.