Title: DHSVM Hillslope Erosion Modeling Theory
1DHSVM Hillslope Erosion Modeling Theory
- Presented by
- Jordan Lanini
- USDA FS DHSVM Sediment Module Demonstration
- August 18, 2004
Photo courtesy of USDA Natural Resources
Conservation Service
2Presentation outline
- Theoretical composition
- Data requirements
- Questions
3Theoretical 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
4Current 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
5Runoff 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
6Kinematic Runoff Routing
- Pixel to pixel overland flow routed using an
explicit finite difference solution of the
kinematic wave approximation to the Saint-Venant
equations - Mannings 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
7Soil particle detachmentRaindrop 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
8Water depth correction
- Standing water diminishes the effects of drop
impact
Wicks Bathurst, 1996
9Soil 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
10Soil 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, different relationships between
cohesion and detachment were examined.
11Soil detachment by runoff (cont.)
12Surface erosion rates in the Eastern Cascades
- Helvey (1980) compiled pre- and post-fire erosion
rates from three experimental watersheds within
the Entiat basin
13Soil detachment by runoff (cont.)
- Rainy Creek scenario analysis
- Relationship was adjusted to observed Cascade
erosion rates - Selected relationship
- Rainy Creek has higher precipitation than Entiat
- Model numbers are total erosion and not delivered
sediment
14Transport 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
15Transport 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.
16Selected 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)
17Limitations 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) -
18Hillslope Sediment Routing
- Sediment is routed using a four-point finite
difference solution of the two-dimensional
conservation of mass equation. - If the pixel contains achannel (including road
side ditches), all sediment and water enters
the channelsegment.
sediment and water
L. Bowling
19Four-point finite difference equation
Detachment (rain and overland flow)
Current time step, current pixel concentration
Previous time step, current pixel mass
Previous time step, upstream pixel mass
Current time step, upstream pixel mass
Current time step, current pixel flow rate
Where ? is a weighting factor, a is
(n/(s0)0.5)3/2 and ß is 3/5.
20Data Input Needed for Hillslope Erosion Model
- Soils
- Bulk Density
- Manning n
- K index
- d50
- cohesion distributions (mean, stand deviation,
minimum value, maximum value)
21Questions?
Photo by Dennis Lettenmaier
22References
- 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,
513-532. - 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)
627-634. - 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, 527-544. - Prosser, I.P. and P. Rustomji 2000 Sediment
transport capcity relations for overland flow,
Progress in Physical Geography 24(2), 179-193. - Smith R.E. and J.Y. Parlange 1978 A
parameter-efficient hydrologic infiltration
model. Wat. Resour. Res. 14(3), 533-538. - 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. p697-732. - 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,
213-238. - 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.