Abstract
Significant advances in upland erosion modeling have been achieved in the past decade. The TREX (Two-dimensional Runoff, Erosion, and Export) watershed model has been developed at Colorado State University for the simulation of surface runoff from spatially and temporally distributed rainstorms on watersheds. The model has been applied in several countries with different climatic conditions. TREX can calculate surface infiltration, surface runoff, sediment transport, and the partition of metals in dissolved, adsorbed, and particulate form. The focus of this chapter is on the calculation of surface flows and total suspended solids at the watershed scale. The chapter is comprised of three parts: (a) a description of the main processes and governing equations, (b) a description of the model components and algorithms, and (c) an application example on a large watershed. The application example for Naesung Stream in South Korea provides powerful visual evidence of upland erosion processes at the watershed scale during large rainstorms (300 mm of rainfall). Model calibration was successful and overall model performance is acceptable. Hydrologic simulation results were in good to very good agreement with measured flow volume, peak flow, and time to peak at the watershed outlet as well as several stations within the watershed. Sediment transport simulation results were also in reasonable agreement with the measured suspended solids concentration.
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Abbreviations
- a :
-
Experimentally determined constant for flocculation
- A :
-
USLE (annual) average soil loss (tons/acre/year) [M L−2 T−1]
- A c :
-
Cross-sectional area of flow [L2]
- B e :
-
Width of eroding surface in flow direction [L]
- B x , B y :
-
Flow width in the x- or y-direction [L]
- \( \widehat{C} \) :
-
USLE soil cover factor [dimensionless]
- C s :
-
Concentration of sediment particles in the water column [M L−3]
- C sb :
-
Concentration of sediment particles in the soil or sediment bed [M L−3]
- C t :
-
Concentration of entrained sediment at the transport capacity [M L−3]
- C w :
-
Concentration of entrained sediment particles by weight at the transport capacity [dimensionless]
- d f :
-
Median floc diameter (μm) [L]
- d p :
-
Particle diameter [L]
- d * :
-
Dimensionless particle diameter [dimensionless]
- f :
-
Infiltration rate [L T−1]
- g :
-
Gravitation acceleration [L T−2]
- G :
-
Particle specific gravity [dimensionless]
- h :
-
Surface water depth (flow depth of water column) [L]
- H c :
-
Capillary pressure (suction) head at the wetting front [L]
- i e :
-
Excess precipitation rate [L T−1]
- i n :
-
Net (effective) rainfall rate at the surface [L T−1]
- J c :
-
Sediment transport capacity areal flux [M L−2 T−1]
- J d :
-
Deposition flux [M L−2 T−1]
- J e :
-
Erosion flux [M L−2 T−1]
- k :
-
Empirically or theoretically derived coefficient for sediment transport capacity [M L−1 T−1]
- \( \widehat{K} \) :
-
USLE soil erodibility factor [dimensionless]
- K h :
-
Effective hydraulic conductivity [L T−1]
- LS :
-
Slope length-gradient factor normalized to a field with a standard length of 23.2 m (76.2 ft) and a slope of 9 % [dimensionless]
- m :
-
Experimentally determined constant for flocculation
- n :
-
Manning roughness coefficient [T L−1/3]
- P c :
-
Wetted perimeter of channel flow [L]
- \( \widehat{P} \) :
-
USLE soil management practice factor [dimensionless]
- P dep :
-
Probability of deposition [dimensionless]
- q :
-
Unit flow rate of water = v a h [L2 T−1]
- q c :
-
Critical unit flow for erosion (for the aggregate soil matrix) [L2 T−1]
- q l :
-
Lateral unit flow from overland plane to channel (floodplain) [L2 T−1]
- q p :
-
Peak runoff rate (m3/s) [L3 T−1]
- q s :
-
Total sediment transport capacity (kg/m s) [M L−1 T−1]
- q x , q y :
-
Unit discharge in the x- or y-direction = Q x /B x , Q y /B y [L2 T−1]
- Q :
-
Total discharge [L3 T−1]
- Q v :
-
Storm runoff volume (m3) [L3]
- Q x , Q y :
-
Flow in the x- or y-direction [L3 T−1]
- R :
-
Rainfall erosivity factor [dimensionless]
- R h :
-
Hydraulic radius of flow = A c/P [L]
- S f :
-
Friction slope [dimensionless]
- S fx , S fy :
-
Friction slope (energy grade line) in the x- or y-direction [dimensionless]
- S 0x , S 0y :
-
Ground surface slope in the x- or y-direction [dimensionless]
- t :
-
Time [T]
- v a :
-
Advective (flow) velocity (in the x- or y-direction) [L T−1]
- v c :
-
Critical velocity for soil or sediment erosion [L T−1]
- v r :
-
Resuspension (erosion) velocity [L T−1]
- v s :
-
Quiescent settling velocity [L T−1]
- v se :
-
Effective settling (deposition) velocity [L T−1]
- v sf :
-
Floc settling velocity (cm/s) [L T−1]
- Y e :
-
MUSLE sediment yield from an individual storm [M]
- α c :
-
Empirical soil erosion coefficient = 11.8
- α x , α y :
-
Resistance coefficient for flow in the x- or y-direction [L1/3 T−1]
- β :
-
Resistance exponent = 5/3 (assuming Manning resistance) [dimensionless]
- β e :
-
Empirical soil erosion exponent = 0.56 [dimensionless]
- β s :
-
Empirically or theoretically derived exponent for discharge [dimensionless]
- γ s :
-
Empirical or theoretically derived exponent for local energy gradient [dimensionless]
- θ :
-
Initial soil moisture deficit [dimensionless]
- ρ b :
-
Bulk density of sediments [M L−3]
- ν :
-
Kinematic viscosity of water [L2 T−1]
References
Green WH, Ampt GA (1911) Studies on soil physics. 1: The flow of air and water through soils. J Agric Sci 4(1):11–24
Richards LA (1931) Capillary conduction of liquids in porous mediums. Physics 1:318–333
Philip JR (1957) The theory of infiltration: 1. The infiltration equation and its solution. Soil Sci 83:345–357
Smith RE, Parlange J-Y (1978) A parameter efficient hydrologic infiltrations model. Water Resour Res 14(3):533–538
Julien PY, Saghafian B, Ogden FL (1995) Raster-based hydrologic modeling of spatially-varied surface runoff. J Am Water Resour Assoc 31(3):523–536
Julien PY (2002) River mechanics. Cambridge University Press, Cambridge, UK, p 434
Julien PY, Simons DB (1985) Sediment transport capacity of overland flow. Trans Am Soc Agric Eng 28(3):755–762
Julien PY, Frenette M (1985) Modeling of rainfall erosion. J Hydraul Eng 11(10):1344–1359
Aksoy H, Kavvas ML (2005) A review of hillslope and watershed scale erosion and sediment transport models. Catena 64(2–3):247–271
Merritt WS, Letcher RA, Jakeman AJ (2003) A review of erosion and sediment transport models. Environ Model Softw 18(8–9):761–799
Wischmeier WH, Smith DD (1978) Predicting soil erosion losses: a guide to conservation planning, vol 537, Agricultural handbook. U.S. Department of Agriculture, Washington, DC, p 58
Renard KG, Foster GR, Weesies GA, Porter JP (1991) RUSLE: revised universal soil loss equation. J Soil Water Conserv 46(1):30–33
Renard KG, Foster GR, Yoder DC, McCool DK (1994) RUSLE revisited: status, questions, answers, and the future. J Soil Water Conserv 49(3):213–220
Renard KG, Foster GR, Weesies GA, McCool DK, Yoder DC (1997) Predicting soil erosion by water: a guide to conservation planning with the revised universal soil loss equation (RUSLE), vol 703, Agricultural handbook. U.S. Department of Agriculture, Washington, DC, p 407
Foster GR, Toy TE, Renard KG (2003) Comparison of the USLE, RUSLE1.06 and RUSLE2 for application to highly disturbed lands. In: Renard KG, McIlroy SA, Gburek WJ, Cranfield HE, Scott RL (eds) First interagency conference on research in watersheds. U.S. Department of Agriculture, Washington, DC
Williams JR (1975) Sediment routing for agricultural watersheds. Water Resour Bull 11(5):965–974
Kinnell PIA (2010) Event soil loss, runoff and the Universal Soil Loss Equation family of models: a review. J Hydrol 385(1–4):384–397
Prosser IP, Rustomji P (2000) Sediment transport capacity relations for overland flow. Prog Phys Geogr 24(2):179–193
Julien PY (2010) Erosion and sedimentation, 2nd edn. Cambridge University Press, Cambridge, UK, p 371
Kilinc MY, Richardson EV (1973) Mechanics of soil erosion from overland flow generated by simulated rainfall, vol 63, Hydrology papers. Colorado State University, Fort Collins, CO
Meyer LD, Wischmeier WH (1969) Mathematical simulation of the process of soil erosion by water. Trans Am Soc Agric Eng 12(6):754–762
Yang CT (1996) Sediment transport: theory and practice. McGraw-Hill Inc., New York, p 396
Engelund F, Hansen E (1967) A monograph on sediment transport in alluvial streams. Teknisk Vorlag, Copenhagen, Denmark, p 62
Cheng NS (1997) Simplified settling velocity formula for sediment particle. J Hydraul Eng 123(2):149–152
Burban PY, Xu Y, McNeil J, Lick W (1990) Settling speeds of flocs in fresh and sea waters. J Geophys Res C Oceans 95(C10):18213–18220
Krishnappan BG (2000) In situ distribution of suspended particles in the Frasier River. J Hydraul Eng 126(8):561–569
Haralampides K, McCorquodale JA, Krishnappan BG (2003) Deposition properties of fine sediment. J Hydraul Eng 129(3):230–234
Krone RB (1962) Flume studies of the transport of sediments in estuarial shoaling processes. Final Report, Hydraulic Engineering Laboratory and Sanitary Engineering Research Laboratory, University of California, Berkeley, California
Beuselinck L, Govers G, Steegen A, Quine TA (1999) Sediment transport by overland flow over an area of net deposition. Hydrol Process 13(17):2769–2782
Mehta A, McAnally W, Hayter E, Teeter A, Heltzel S, Carey W (1989) Cohesive sediment transport. II: Application. J Hydraul Eng 115(8):1094–1112
Singh VP (1995) Computer models of watershed hydrology. Water Resources Publications, Highlands Ranch, CO, p 1144
Julien PY, Saghafian B (1991) CASC2D user’s manual—A two dimensional watershed rainfall-runoff model. Report CER90-91PYJ-BS-12. Department of Civil Engineering, Colorado State University, Fort Collins, Colorado, p 66
Johnson BE, Julien PY, Molnar DK, Watson CC (2000) The two-dimensional upland erosion model CASC2D-SED. J Am Water Resour Assoc 36(1):31–42
Ogden FL, Julien PY (2002) CASC2D: a two-dimensional, physically-based, hortonian hydrologic model. In: Singh VP, Frevert D (eds) Mathematical models of small watershed hydrology and applications. Water Resources Publications, Littleton, CO, pp 69–112
Julien PY, Rojas R (2002) Upland erosion modeling with CASC2D-SED. Int J Sediment Res 17(4):265–274
Downer CW, Ogden FL (2004) GSSHA: model to simulate diverse stream flow producing processes. J Hydrol Eng 9(3):161–174
Abbott MB, Bathurst JC, Cunge JA, O’Connell PE, Rasmussen J (1986) An introduction to the European Hydrological System—Système Hydrologique Europèen, SHE.1: History and philosophy of a physically-based, distributed modelling system. J Hydrol 87(1–2):45–59
Wicks JM, Bathurst JC (1996) SHESED: a physically based, distributed erosion and sediment yield component for the SHE hydrological modeling system. J Hydrol 175(1–4):213–238
Ewen J, Parkin G, O’Connell PE (2000) SHETRAN: distributed river basin flow and transport modeling system. J Hydrol Eng 5(3):250–258
Abbott MB, Bathurst JC, Cunge JA, O’Connell PE, Rasmussen J (1986) An introduction to the European Hydrological System—Système Hydrologique Europèen, SHE. 2: Structure of a physically-based, distributed modelling system. J Hydrol 87(1–2):61–77
Velleux M, England J, Julien P (2008) TREX: spatially distributed model to assess watershed contaminant transport and fate. Sci Total Environ 404(1):113–128
England J, Velleux M, Julien P (2007) Two-dimensional simulations of extreme floods on a large watershed. J Hydrol 347(1):229–241
Velleux M (2005) Spatially distributed model to assess watershed contaminant transport and fate. Ph.D. dissertation, Department of Civil Engineering, Colorado State University, Fort Collins, Colorado, p 261
Rojas R (2002) GIS-based upland erosion modeling, geovisualization and grid size effects on erosion simulations with CASC2D-SED. Ph.D. dissertation, Department of Civil Engineering, Colorado State University, Fort Collins, Colorado
Molnár DK, Julien PY (2000) Grid size effects on surface runoff modeling. J Hydrol Eng 5(1):8–16
Velleux M, Julien P, Rojas-Sanchez R, Clements W, England J (2006) Simulation of metals transport and toxicity at a mine-impacted watershed: California Gulch, Colorado. Environ Sci Technol 40(22):6996–7004
Ambrose RB, Martin JL, Wool TA (1993) WASP5, a hydrodynamic and water quality model—model theory, user’s manual, and programmer’s guide. U.S. Environmental Protection Agency, Office of Research and Development, Environmental Research Laboratory, Athens, GA
Velleux M, Westenbroek S, Ruppel J, Settles M, Endicott D (2001) A user’s guide to IPX, the in-place pollutant export water quality modeling framework, Ver. 2.7.4. EPA/600/R-01/079. U.S. Environmental Protection Agency, Office of Research and Development, National Health and Environmental Effects Research Laboratory, Mid-Continent Ecology Division, Large Lakes Research Station, Grosse Ile, Michigan, p 179
MJU (2010) Naesung stream watershed data collection. Prepared by Myongji University, Yongin, South Korea
MJU (2011) Naesung stream watershed bank erosion. Prepared by Myongji University, Yongin, South Korea
ESRI (2008) ArcGIS 9.3. Environmental Systems Research Institute, Redlands, CA
USACE (2008) HEC-RAS, river analysis system user’s manual, version 4.0. U.S. Army Corps of Engineers, Hydrologic Engineering Center (HEC), Davis, CA
Rojas R, Velleux M, Julien P, Johnson B (2008) Grid scale effects on watershed soil erosion models. J Hydrol Eng 13(9):793–802
Tarboton D (1997) A new method for the determination of flow directions and upslope areas in grid digital elevation models. Water Resour Res 33(2):309–319
Jia Y, Kinouchi T, Yoshitani J (2005) Distributed hydrologic modeling in a partially urbanized agricultural watershed using water and energy transfer process model. J Hydrol Eng 10(4):253–263
Linsley RK, Kohler MA, Paulhus JLH (1982) Hydrology for engineers, 3rd edn. McGraw-Hill Book Company, New York, p 508
Woolhiser DA, Smith RE, Goodrich DC (1990) KINEROS, a kinematic runoff and erosion model: documentation and user manual. U.S. Department of Agriculture, Agriculture Research Service, ARS-77, Mar 1990
Bras RL (1990) Hydrology: an introduction to hydrologic science. Addison-Wesley Publishing Company, Reading, MA, p 643
USACE (1998) HEC-1 flood hydrograph package user’s manual. Report: CPD-1A. U.S. Army Corps of Engineers, Hydraulic Engineering Center, Davis, CA, June 1998
Chow VT (1959) Open-channel hydraulics. McGraw-Hill, New York, p 680, Reissued 1988
Rawls WJ, Ahuja LR, Brakensiek DL, Shirmohammadi A (1993) Infiltration and soil movement. In: Maidment DR (ed) Handbook of hydrology. McGraw-Hill, Inc., New York, pp 5.1–5.51
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Julien, P.Y., Velleux, M.L., Ji, U., Kim, J. (2014). Upland Erosion Modeling. In: Wang, L., Yang, C. (eds) Modern Water Resources Engineering. Handbook of Environmental Engineering, vol 15. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-595-8_9
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