2018 SWCS International Annual Conference July 29-August 1, 2018 Albuquerque Convention Center

1. Slope-Velocity-
Equilibrium and
evolution of surface
roughness on stony
hillslopes
MARK A. NEARING1, VIKTOR O. POLYAKOV1, MARY
H. NICHOLS1, MARIANO HERNANDEZ1, LI LI2, YING
ZHAO2, GERARDO ARMENDARIZ1
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

2. 13 Years Rainfall Simulation
on western rangeland
What is the source
of velocity variability?
1. Runoff
272 experiments,
23 sites

3. Velocity vs. Runoff
coded by slope

4. Velocity vs. Runoff
coded by ground cover

5. R-
Square
Variables in
Model
R-
Square
Variables in
Model
0.4120 runoff 0.0864 foliar grass
0.2909 litter 0.0593 foliar shrub
0.2439 ground cover
total
0.0488 foliar total
0.1831 basal gap
fraction
0.0225 basal
0.1625 basal gap av.
length
0.0049 canopy gap av.
length
0.1484 rock 0.0025 slope
0.1079 canopy gap
fraction
0.0010 foliar forbs

6. 𝑽 =
𝟏
𝒏
𝑹 𝟐/𝟑
𝑺 𝟏/𝟐
𝑽 = 𝑪(𝑹𝑺) 𝟏/𝟐

7. Slope-Velocity-Equilibrium
is a state of a soil surface that:
1. evolves naturally over time due to the
interaction between overland flow and surface
morphology,
2. wherein steeper areas develop a relative
increase in physical and hydraulic roughness
3. such that flow velocity is a function of
overland flow rate independent of slope
gradient.

8. Methods:
1. Artificial rainfall was applied to 2m by 6m plots
at 5%, 12%, and 20% slope gradients.
2. Measurements of runoff rate, velocity, rock
cover, and surface roughness.
Hypothesis:
Velocities measured at the end of each
experiment were a unique function of discharge
rates, independent of slope gradient or rainfall
intensity.

11. Velocity with Dye and Salt
Rock Cover by size

12. Plot-average rock cover (>0.5 cm) as a
function of cumulative runoff for the 6
experiments.

13. Flow velocities down the full
plot as a function of
cumulative runoff depth for:
a) I=59 mm hr-1, and b) I=178
mm hr-1.

14. Final flow velocities for all 6 experiments at each of the three velocity
transect measurement transects and two rainfall rates.

15. 𝑽 =
𝟏
𝒏
𝑹 𝟐/𝟑
𝑺 𝟏/𝟐
𝑽 = 𝑪(𝑹𝑺) 𝟏/𝟐
V = 26.39 q0.696 (r2 = 0.95, n = 36)

16. • This study supports the hypothesis of slope-velocity-
equilibrium
• Physical surface roughness was greater at steeper slopes.
• Hydraulic roughness was greater at steeper slopes.
• Velocities measured at the end of each experiment were a
unique function of discharge rates, independent of slope
gradient or rainfall intensity.
• Hydraulic equations, such as Chezy and Manning, in
hillslope scale runoff models are problematic because the
coefficients vary with slope and rainfall intensity.

17. The long drive home