Articles | Volume 21, issue 6
Hydrol. Earth Syst. Sci., 21, 3221–3229, 2017
Hydrol. Earth Syst. Sci., 21, 3221–3229, 2017

Research article 30 Jun 2017

Research article | 30 Jun 2017

Slope–velocity equilibrium and evolution of surface roughness on a stony hillslope

Mark A. Nearing1, Viktor O. Polyakov1, Mary H. Nichols1, Mariano Hernandez1, Li Li2, Ying Zhao2, and Gerardo Armendariz1 Mark A. Nearing et al.
  • 1USDA-Agricultural Research Service, Southwest Watershed Research Center, Tucson, AZ 85719, USA
  • 2School of Natural Resources and the Environment, University of Arizona, Tucson, AZ 85705, USA

Abstract. Slope–velocity equilibrium is hypothesized as a state that evolves naturally over time due to the interaction between overland flow and surface morphology, wherein steeper areas develop a relative increase in physical and hydraulic roughness such that flow velocity is a unique function of overland flow rate independent of slope gradient. This study tests this hypothesis under controlled conditions. Artificial rainfall was applied to 2 m by 6 m plots at 5, 12, and 20 % slope gradients. A series of simulations were made with two replications for each treatment with measurements of runoff rate, velocity, rock cover, and surface roughness. Velocities measured at the end of each experiment were a unique function of discharge rates, independent of slope gradient or rainfall intensity. Physical surface roughness was greater at steeper slopes. The data clearly showed that there was no unique hydraulic coefficient for a given slope, surface condition, or rainfall rate, with hydraulic roughness greater at steeper slopes and lower intensities. This study supports the hypothesis of slope–velocity equilibrium, implying that use of hydraulic equations, such as Chezy and Manning, in hillslope-scale runoff models is problematic because the coefficients vary with both slope and rainfall intensity.

Short summary
This study presents novel scientific understanding about the way that hillslope surfaces form when exposed to rainfall erosion, and the way those surfaces interact with and influence runoff velocities during rain events. The data show that hillslope surfaces form such that flow velocities are independent of slope gradient and dependent on flow rates alone. This result represents a shift in thinking about surface water runoff.