1. DHSVM Hillslope Erosion Modeling Theory
Presented by:
Jordan Lanini
USFS DHSVM Sediment Module Demonstration
August 18, 2004
Photo courtesy of USDA Natural Resources Conservation Service

2. Presentation outline Surface erosion rates in the Cascades
Theoretical composition
Data requirements

3. Surface erosion rates in the Cascades
Photo by Dennis Lettenmaier

4. Surface erosion rates in the Eastern Cascades
Helvey (1980) compiled pre- and post-fire erosion rates from three experimental watersheds within the Entiat basin
Erosion rate kg/ha
Watershed
1967
1968
1969
1970
Comments
Fox 70
100 71 21
Burns 10
Mean values based on 10-year accumulation
McCree 8
Mean 29 39 13

5. Theoretical Background
Hillslope erosion consists of three components:
Detachment
Transport
Deposition
Requires kinematic runoff routing to calculate erosion and transport
raindrop
impact
leaf drip
impact
shearing by overland flow
Mechanisms of Soil Particle Detachment
L. Bowling, J. Lanini, N. Voisin

6. Current DHSVM Runoff Generation and Routing
Runoff is produced via:
Saturation excess (pixels 6 and 7)
Infiltration excess based on a user-specified static maximum infiltration capacity (pixel 3)
Runoff is routed to the downslope neighbors one pixel/time step

7. Runoff Generation – Dynamic Infiltration Excess
Calculation of maximum infiltration capacity:
The first timestep there is surface water on the pixel, all surface water infiltrates.
If there is surface water in the next timestep, the maximum infiltration capacity is calculated based on the amount previously infiltrated.
Dominant form of runoff generation on unpaved roads and post burn land surfaces
N. Voisin

8. Kinematic Runoff Routing
Pixel to pixel overland flow routed using an explicit finite difference solution of the kinematic wave approximation to the Saint-Venant equations
Manning’s equation is used to solve for flow area in terms of discharge
Per DHSVM timestep, a new solution sub-timestep is calculated satisfying the Courant condition, which is necessary for solution stability.
L. Bowling

9. Soil particle detachment: Raindrop and leaf drip impact
Where
is soil detached by raindrop impact in kg m-2 s-1,
is a raindrop soil erodibility coefficient (J-1),
is the portion of ground covered by understory,
is the portion of canopy cover for each grid cell,
is the square of raindrop momentum, and
is the square of leaf drip momentum.
Wicks & Bathurst, 1996
Photo courtesy of USDA Natural Resources Conservation Service

10. Water depth correction
Standing water diminishes the effects of drop impact
Wicks & Bathurst, 1996

11. Soil detachment by runoff
Modeled with transport capacity (TC) as a balance between erosion and deposition.
Where:
is a flow detachment efficiency coefficient. This reduces erosion for cohesive soils;
is the flow width;
is particle settling velocity;
is sediment concentration.
Morgan et al, 1998

12. Soil detachment by runoff (cont.)
Flow detachment efficiency:
during deposition
for cohesive soils during detachment:
From Wicks & Bathurst but detachment decreases too quickly with increased cohesion.
Therefore, diffferent relationships between cohesion and detachment were examined.

13. Soil detachment by runoff (cont.)

14. Soil detachment by runoff (cont.)
Rainy Creek scenario analysis
Relationship was adjusted for to observed Cascade erosion rates
Selected relationship:
Detachment
Erosion rate
Relationship
kg/ha/year
β=0.79(e-0.85C)
14.48
β=1/C
11,255
β=1/C2
8,175
β=1/C3
2,730
β=0.79(e-0.6C)
510

15. Transport Capacity
Numerous equations exist for transport in overland flow, but…
There is no silver bullet.
Three main types of transport capacity equations:
Unit stream power;
Mean stream power;
Shear stress.
Prosser & Rustomji, 2000
Photo courtesy of USDA Natural Resources Conservation Service

16. Transport capacity (cont)
How to decide?
Govers (1992) compiled data from transport capacity studies and evaluated several equations for overland flow application.
Govers found that no existing equation worked well over a wide range of particle sizes and slopes.
Govers saw good results from a unit stream power equation with a threshold and a correction for particle diameter.

17. Selected transport capacity relationship
Kineros (Woolhiser) relationship
Contains unit stream power threshold and particle diameter adjustment
is the density of water;
d is the particle diameter;
S is the slope;
H is the flow depth;
is a critical unit stream power value (0.004 m/s);

18. Limitations on transport capacity
Govers (1992) found maximum transport capacities of 0.35 m3/ m3 during flume experiments
Model limits transport calculations to flow depths greater than 1 mm (Woolhiser relationship results in excessive TC below this threshold)

19. Hillslope Sediment Routing
Sediment is routed using a four-point finite difference solution of the two-dimensional conservation of mass equation.
If the pixel contains a channel (including road side ditches), all sediment and water enters the channel segment.
sediment and water
L. Bowling

20. Four-point finite difference equation
Current time step, current pixel concentration
Previous time step, current pixel mass
Detachment
(rain and overland flow)
Previous time step, upstream pixel mass
Current time step, upstream pixel mass
Current time step, current pixel flow rate
Where θ is a weighting factor, α is (n/(s0)0.5)3/2 and β is 3/5.

21. Data Input Needed for Hillslope Erosion Model
Soils: Bulk Density, Manning n, K index, d50, distributions (mean, stand deviation, minimum value, maximum value) of Cohesion

22. References
Bagnold, R.A., 1966, An approach of sediment transport model from general physics. US Geol. Survey Prof. Paper 422-J.
Epema G.F., H. Th. Riezebos 1983: Fall Velocity of waterdrops at different heights as a factor influencing erosivity of simulated rain. Rainfall simulation, Runoff and Soil Erosion. Catena suppl. 4, Braunschweig. Jan de Ploey (Ed).
Everaert, W., 1991, Empirical relations for the sediment transport capacity of interill flow, Earth Surface Processes and Landforms, 16,
Govers, G., 1992: Evaluation of transporting capacity formulae for overland flow, In: Overland Flow: Hydraulics and Erosion Mechanics, Parsons J.A. and Abrahams A.D. Eds. UCL Press Limited, London.
Helvey, J.D. 1980, Effects of a North Central Washington wildfire on runoff and sediment production, Water Resources Bulletin, 16(4)
Morgan, R.P.C., J.N. Qinton, R.E. Smith, G. Govers, J.W.A. Poesen, K. Auerswald, G. Chisci, D. Torri and M.E. Styczen, 1998, The European soil erosion model (EUROSEM): a dynamic approach for predicting sediment transport from fields and small catchments, Earth Surface Processes and Landforms, 23,
Prosser, I.P. and P. Rustomji 2000: Sediment transport capcity relations for overland flow, Progress in Physical Geography 24(2),
Smith R.E. and J.Y. Parlange 1978: A parameter-efficient hydrologic infiltration model. Wat. Resour. Res. 14(3),
Smith R.E., D.C. Goodrich, D.A. Woolhiser, and C.L. Unkrich 1995: KINEROS – a kinematic runoff and erosion model. Chapter 20 in: Computer Models of Watershed Hydrology, Water Resources Publication, Highland Ranch, Colorado. p
Wicks, J.M. and J.C. Bathurst, 1996, SHESED: a physically based, distributed erosion and sediment yield component for the SHE hydrological modeling system, Journal of Hydrology, 175,
Woolhiser, D.A., R.E. Smith and D.C. Goodrich, 1990, KINEROS, A kinematic runoff and erosion model: documentation and user manual, USDA-Agricultural Research Service, ARS-77, 130 pp.