DHSVM Hillslope Erosion Modeling Theory Presented by: Jordan Lanini USFS DHSVM Sediment Module Demonstration August 18, 2004 Photo courtesy of USDA Natural Resources Conservation Service

Presentation outline Surface erosion rates in the Cascades Theoretical composition Data requirements

Surface erosion rates in the Cascades Photo by Dennis Lettenmaier

Surface erosion rates in the Eastern Cascades Helvey (1980) compiled pre- and post-fire erosion rates from three experimental watersheds within the Entiat basin Erosion rate kg/ha Watershed 1967 1968 1969 1970 Comments Fox 70 100 71 21   Burns 10 Mean values based on 10-year accumulation McCree 8 Mean 29 39 13

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

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

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

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 Manning’s 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

Soil particle detachment: Raindrop 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

Water depth correction Standing water diminishes the effects of drop impact Wicks & Bathurst, 1996

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

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, diffferent relationships between cohesion and detachment were examined.

Soil detachment by runoff (cont.)

Soil detachment by runoff (cont.) Rainy Creek scenario analysis Relationship was adjusted for to observed Cascade erosion rates Selected relationship: Detachment Erosion rate Relationship kg/ha/year β=0.79(e-0.85C) 14.48 β=1/C 11,255 β=1/C2 8,175 β=1/C3 2,730 β=0.79(e-0.6C) 510

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

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.

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);

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)

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 a channel (including road side ditches), all sediment and water enters the channel segment. sediment and water L. Bowling

Four-point finite difference equation Current time step, current pixel concentration Previous time step, current pixel mass Detachment (rain and overland flow) Previous time step, upstream pixel mass Current time step, upstream pixel mass Current time step, current pixel flow rate Where θ is a weighting factor, α is (n/(s0)0.5)3/2 and β is 3/5.

Data Input Needed for Hillslope Erosion Model Soils: Bulk Density, Manning n, K index, d50, distributions (mean, stand deviation, minimum value, maximum value) of Cohesion

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.