DHSVM Channel Erosion and
Transport Model
Presented by:
Jordan Lanini
USFS DHSVM Sediment Module Demonstration
August 18, 2004
Photo by US Geological Survey
Colleen O. Doten, University of Washington
Laura C. Bowling, Purdue University
Edwin D. Mauer, Santa Clara University
Jordan S. Lanini, University of Washington
Nathalie Voisin, University of Washington
Dennis P. Lettenmaier, University of Washington
Presentation outline
• Channel routing and overview
• Theoretical background
• Model description
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
Sediment supply
Upstream
Channel
Segment
Hillslope
Erosion
Mass
Wasting
Road Surface
Erosion
http://www.shelales.com/peru_photos1.htm
• Sediment is tracked by
particle size
• Mass wasting supply:
– fixed lognormally
distributed grain size
distribution which is a
function of the userspecified 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
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
Bagnold’s approach for total sediment load.
E. Maurer
Channel routing concepts
• Based on Exner (1925) equation:
Sediment
concentration
Sediment
density


mS 
AcVS  s   s q s
t
x
Sediment velocity
Mass change of
sediment in channel
segment
E. Maurer
Cross-sectional
area
Mass sediment
inflow rate
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.
Channel sediment routing (cont)
• Each particle size is routed individually
• Sediment transport capacity is calculated
according to the Bagnold (1966) approach
for total load:
 eb
V 
TC c   
 0.01

tan

V
ss 

• Where:
– TCc is the sediment transport capacity
– eb is a function of velocity
Transport capacity (cont)
– tan α is a function of dimensionless shear
– V is the mean flow velocity
– Vss is the sediment settling velocity
– ω is the stream power per unit bed area:
  gDSV
• D is the flow depth
• S is the energy gradient (assumed to be the
channel slope
Channel sediment routing (cont)
• Convert transport capacity to dry mass flow rate
Qs 
TC

g(1 - )
s
• Calculate maximum bed degradation rate

M s   Qs B D  1   Qs B U
t
– D is current channel segment, U is upstream
segment
– Ф is a space weighting factor
Four-point finite difference equation
Current time step, current
channel mass flow rate
Previous time step, current
channel segment mass flow rate
Mass sediment inflow rate
 AcVs  s tD1  1   AcVs  s Ut 1  1    AcVs  s tD   AcVs  s Ut    s q s x 

Current time step, upstream
channel segment mass flow rate


Ms
t

Previous time step,
upstream channel
segment mass flow rate
Bed degradation rate
Where θ is a weighting factor
Notes about the numerical
performance
• The weighting factors θ and Ф 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.
References
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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, 165–180.
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.