DHSVM Hillslope Erosion Modeling Theory

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DHSVM 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
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Presentation outline

• Theoretical composition
• Data requirements
• Questions

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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
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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

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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
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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
• 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
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Soil 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
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Water depth correction

• Standing water diminishes the effects of drop
  impact

Wicks Bathurst, 1996
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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
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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, different relationships between
  cohesion and detachment were examined.

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Soil detachment by runoff (cont.)
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Surface erosion rates in the Eastern Cascades

• Helvey (1980) compiled pre- and post-fire erosion
  rates from three experimental watersheds within
  the Entiat basin

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Soil 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

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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
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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.

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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)

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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)

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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 achannel (including road
  side ditches), all sediment and water enters
  the channelsegment.

sediment and water
L. Bowling
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Four-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.
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Data Input Needed for Hillslope Erosion Model

• Soils
• Bulk Density
• Manning n
• K index
• d50
• cohesion distributions (mean, stand deviation,
  minimum value, maximum value)

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Questions?
Photo by Dennis Lettenmaier
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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,
  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.