DHSVM Channel Erosion and Transport Model

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DHSVM Channel Erosion and Transport Model
Presented by Jordan Lanini USFS DHSVM Sediment
Module Demonstration August 18, 2004
Colleen O. Doten, University of WashingtonLaura
C. Bowling, Purdue UniversityEdwin D. Mauer,
Santa Clara UniversityJordan S. Lanini,
University of Washington Nathalie Voisin,
University of WashingtonDennis P. Lettenmaier,
University of Washington
Photo by US Geological Survey
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Presentation outline

• Channel routing and overview
• Theoretical background
• Model description

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Channel routing-overview

• Sediment Supply
• channel sediment storage from the MWM
• lateral inflow from hillslope and roads
• upstream channel segment
• Sediment particles
• have a constant lognormally distributed grain
  size which is a function of the user-specified
  median grain size diameter (d50) and d90
• are binned into a user-specified number of grain
  size classes

E. Maurer
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Sediment supply

• Sediment is tracked by particle size
• Mass wasting supply
• fixed lognormally distributed grain size
  distribution which is a function of the
  user-specified median grain size diameter (d50)
  and d90.
• particles are binned into a user-specified number
  of sediment size classes
• Hillslope and road surface supply added to class
  based on d50

Upstream Channel Segment
Hillslope Erosion
Mass Wasting
Road Surface Erosion

• http//www.shelales.com/peru_photos1.htm

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Channel routing requirements

• Sediment is routed using a four-point finite
  difference solution of the two-dimensional
  conservation of mass equation.
• Instantaneous upstream and downstream flow rates
  are used in the routing.
• Transport depends on
• available sediment in each grain size class, and
• capacity of flow for each grain size calculated
  using Bagnolds approach for total sediment load.

E. Maurer
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Channel routing concepts

• Based on Exner (1925) equation

Sediment concentration
Sediment density
Sediment velocity
Mass change of sediment in channel segment
Cross-sectional area
Mass sediment inflow rate
E. Maurer
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Channel routing concepts (cont)

• A time step is selected for numerical stability
  with a Courant number (Vs?t/?x ) of 1.
• Sub-timestep flow rates are calculated using the
  previously routed flow for that timestep.
• Lateral and upstream sediment inflows are
  calculated for the timestep.

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Channel sediment routing (cont)

• Each particle size is routed individually
• Sediment transport capacity is calculated
  according to the Bagnold (1966) approach for
  total load
• Where
• TCc is the sediment transport capacity
• eb is a function of velocity

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Transport capacity (cont)

• tan a is a function of dimensionless shear
• V is the mean flow velocity
• Vss is the sediment settling velocity
• ? is the stream power per unit bed area
• D is the flow depth
• S is the energy gradient (assumed to be the
  channel slope

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Channel sediment routing (cont)

• Convert transport capacity to dry mass flow rate
• Calculate maximum bed degradation rate
• D is current channel segment, U is upstream
  segment
• ? is a space weighting factor

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Four-point finite difference equation
Previous time step, current channel segment mass
flow rate
Current time step, current channel mass flow rate
Mass sediment inflow rate
Previous time step, upstream channel segment mass
flow rate
Current time step, upstream channel segment mass
flow rate
Bed degradation rate
Where ? is a weighting factor
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Notes about the numerical performance

• The weighting factors ? and ? are used to
  incorporate past values into concentration
  calculations. Wicks and Bathurst recommend a
  value of 0.55 for both.
• When a large disparity exists between the values,
  such as during inflow from a mass wasting event,
  the equation introduces a large mass balance
  error.
• To remedy this, the values are set to 1.0 during
  mass wasting inflows.

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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.
• Exner, F. M., 1925, Über die wechselwirkung
  zwischen wasser und geschiebe in flüssen,
  Sitzungber. Acad. Wissenscaften Wien Math.
  Naturwiss. Abt. 2a, 134, 165180.
• Graf, W., 1971, Hydraulics of Sediment Transport,
  McGraw-Hill, NY, NY, pp. 208-211.
• Komura, W., 1961, Bulk properties of river
  sediments and its application to sediment
  hydraulics, Proc. Jap. Nat. Cong. For Appl. Mech.
• 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.
• Rubey, W.W., 1933, Settling velocities of
  gravels, sands, and silt particles, Am. Journal
  of Science, 5th Series, 25 (148), 325-338.
• Shields, A., 1936, Application of similarity
  principles and turbulence research to bedload
  movement. Hydrodynamic Lab. Rep. 167, California
  Institute of Technology, Pasadena, Calif.
• Sturm, T., 2001, Open Channel Hydraulics,
  McGraw-Hill, NY, NY, pp. 378-380.
• 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.