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Upland Erosion Modeling

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Modern Water Resources Engineering

Part of the book series: Handbook of Environmental Engineering ((HEE,volume 15))

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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]

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Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, CO, USA

    Pierre Y. Julien Ph.D., P.E. & Jaehoon Kim M. Sc.

  2. HDR HydroQual, Mahwah, NJ, USA

    Mark L. Velleux Ph.D., P.H., P.E.

  3. River and Coastal Research, Korea Institute of Construction Technology, Goyang-si, Korea

    Un Ji Ph.D.

Authors
  1. Pierre Y. Julien Ph.D., P.E.
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  2. Mark L. Velleux Ph.D., P.H., P.E.
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  3. Un Ji Ph.D.
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  4. Jaehoon Kim M. Sc.
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Editor information

Editors and Affiliations

  1. Zorex Corporation, Newtonville, New York, USA

    Lawrence K. Wang

  2. Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado, USA

    Chih Ted Yang

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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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  • DOI: https://doi.org/10.1007/978-1-62703-595-8_9

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