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Title: Slope-Velocity-Equilibrium and evolution of surface roughness on a stony hillslope

item Nearing, Mark
item Polyakov, Viktor
item Nichols, Mary
item Hernandez, Mariano
item LI, LI - University Of Arizona
item ZHAO, Y. - University Of Arizona
item Armendariz, Gerardo

Submitted to: Hydrology and Earth System Sciences
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/25/2017
Publication Date: 6/29/2017
Citation: Nearing, M.A., Polyakov, V.O., Nichols, M.H., Hernandez Narvaez, M.N., Li, L., Zhao, Y., Armendariz, G.A. 2017. Slope-Velocity-Equilibrium and evolution of surface roughness on a stony hillslope. Hydrology and Earth System Sciences. 21:3221-3229.

Interpretive Summary: This study presents novel scientific understanding about the way that hillslope surface roughness forms when exposed to rainfall erosion, and the way those surface interact with and influence runoff velocities during rain events. The data clearly show that hillslope surfaces form such that flow velocities are independent of slope gradient, and only dependent on flow rates alone. This result represents a major shift in thinking about surface water runoff, wherein we expect that runoff velocities are dependent on slope gradient as well as runoff depths. In addition to the new scientific understanding of nature presented here, the results have major new implications about how we mathematically model or represent surface water runoff during storm events. Routing of surface water runoff in modern hydrologic models is invariably done using an equation that relates runoff velocity to runoff depth and slope gradient (e.g., Manning or Chezy). This paper suggests that these equations are routinely poorly applied because such applications use constant values of their respective coefficients, whereas the data clearly show that the coefficients must be spatially and temporally variable as a function of both slope gradient, rainfall intensities, and downslope distance. This paper suggests both a guide for possibilities for addressing the variability and a simpler and possibly more accurate modeling procedure. These applications are used in a variety of earth surface applications from watershed management to flood routing.

Technical Abstract: Slope-velocity equilibrium is hypothesized as a state that evolves naturally over time due to the interaction between overland flow and bed 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 2m by 6m plots at 5%, 12%, and 20% slope gradients. A series of simulations were made 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 not a 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.