1. DHSVM Channel Erosion and Transport Model 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 Photo by US Geological Survey Presented by: Jordan Lanini USFS DHSVM Sediment Module Demonstration August 18, 2004

2. Presentation outline Channel routing and overview Theoretical background Model description

3. 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 (d 50 ) and d 90 –are binned into a user-specified number of grain size classes E. Maurer

4. Sediment supply http://www.shelales.com/peru_photos1.htm Road Surface Erosion Mass Wasting Hillslope Erosion Upstream Channel Segment 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 (d 50 ) and d 90. –particles are binned into a user-specified number of sediment size classes Hillslope and road surface supply added to class based on d 50

5. 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

6. Channel routing concepts Based on Exner (1925) equation: E. Maurer Mass change of sediment in channel segment Cross-sectional area Mass sediment inflow rate Sediment concentration Sediment density Sediment velocity

7. 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.

8. 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: –TC c is the sediment transport capacity –e b is a function of velocity

9. Transport capacity (cont) –tan α is a function of dimensionless shear –V is the mean flow velocity –V ss is the sediment settling velocity –ω is the stream power per unit bed area: D is the flow depth S is the energy gradient (assumed to be the channel slope

10. 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 –Ф is a space weighting factor

11. Four-point finite difference equation Bed degradation rate Current time step, current channel mass flow rate Current time step, upstream channel segment mass flow rate Mass sediment inflow rate Previous time step, current channel segment mass flow rate Previous time step, upstream channel segment mass flow rate Where θ is a weighting factor

12. 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.

13. 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, 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.