USLE & Other ModelsUSLE & Other ModelsNREM 461

Dr. Greg BrulandDr. Greg Bruland

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I Universal Soil Loss Equation (USLE)I. Universal Soil Loss Equation (USLE)

A. In math terms Erosion = ƒ[(Erositivity)(Erodibility)]ƒ[( y)( y)]

EROSIVITY ERODIBILITY

MANAGEMENTPHYSICALCHARACTERISTICS

RAINFALL

ENERGYENERGYLANDMGMT

CROPMGMT

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B. USLE developed by scientists at ARS, SCS, Purdue p y , ,Univ. under leadership of Walter Wishmeier

1 1st took form in1. 1st took form in

2. Equation published by Wishmeier & Smith in

3. Developed to predict long-term average annual soil loss from erosion on uniform cultivated fields in eastern U.S.

How universal is it?How universal is it?

Dr. W. Wischmeier

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Wischmeier

USLE Term English Units Metric UnitsUSLE Term English Units Metric UnitsA: avg. annual soil loss

tons/acre-year Mg/hectare-year

R i f ll 100 f ft t i f ll/ (MJ )/(h h )R: rainfall erosivity

100s of ft-tons rainfall/ac-yrrange: 0-2000

(MJ mm)/(ha h yr)range: 0-700

K: soil erodibility tons soil/100 ft tons rainfall (Mg ha h)/(ha MJ mm) yrange: 0.01-0.7

( g ) ( )range: 0.001-0.09

LS: slope length & gradient factor

dimensionlessrange:

dimensionless range:gradient factor range: range:

C: cover-mgmt factor

dimensionless range:

dimensionless range:g g

P: supporting-practice factor

dimensionless range:

dimensionlessrange:

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Components of USLEp

Rainfall Erosivity Factor (R)Rainfall Erosivity Factor (R)

A = R x K x LS x C x PA R x K x LS x C x P

R estimated from maximum 30 minute rainstorm intensity values displayed on map in Troeh pg. 140

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Troeh et al. (2004)

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Soil Erodibility Factor (K)Soil Erodibility Factor (K)

Rate of soil loss on a standard plot 72 6 ftRate of soil loss on a standard plot 72.6 ft (22 m) long with 9% slope

A = R x K x LS x C x P

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K factors tabulated for il i i C tsoil series in County

Soil Surveys

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Slope Length & Steepness gFactor (LS)

R ti f il l it f l t ithRatio of soil loss per unit area of plot with slope X, compared to what would be lost f f ll 72 6 ft l l t ith 9%from a fallow 72.6-ft-long plot with 9% slope (can be <1 or >1)

A = R x K x LS x C x P

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LS can be determined from lookup tables or from the empirical equation:

LS = (x/22.13)n (0.065 + 0.045s + 0.0065s2)

Where x =Where x =s =n = empirical parameter that should be varied

based on slope steepness

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Cover-Management Factor (C)Cover Management Factor (C)

Ratio of soil loss under specificRatio of soil loss under specific cover conditions compared to fallow

A = R x K x LS x C x P

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Supporting-Practice (P) FactorSupporting Practice (P) Factor

The fractional amount of erosion thatThe fractional amount of erosion that occurs when “special practices,” i.e. contour cultivation contour strip croppingcontour cultivation, contour strip cropping, & terracing are used compared to erosion that would occur w/o themthat would occur w/o them

A = R x K x LS x C x P

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4. Notes about USLE

a. USLE is an empirical equation based on measurements rather than theoryeasu e e ts at e t a t eo y

b. Designed for Eastern U.S. needs to be reparameterizedreparameterized

c. Provides annual estimates-

d. Interdependence among variables & nonlinear p grelationships

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Example USLE Calculations

With conventional tillage:A= 170 x 0.26 x 1.62 x 0.20 x 1.0 = 14.3 t/a-yy

With contour cultivation:A= 170 x 0.26 x 1.62 x 0.20 x 0.61 = 8.7 t/a-y

With conservation tillage & contouring:With conservation tillage & contouring:A = 170 x 0.26 x 1.62 x 0.11 x 0.61 = 4.8 t/a-y

With conventional tillage & terracing:A = 170 x 0 26 x 0 60 x 0 20 x 1 0 = 5 3 t/a-y

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A 170 x 0.26 x 0.60 x 0.20 x 1.0 5.3 t/a y

C.MUSLE (Modified USLE 1978)

1. R: expanded to cover western U.S. including HI (20-450), but not AK450), but not AK

2. K: erodibility nomograph developed based on clay, silt, sand OM structure & permeabilitysand, OM, structure, & permeability

3. LS: adapted to handle multi-segmented slopes

4. C: expanded to 6 crop stage periods, C values provided forfor

5. P: not changed for contour cult, & contour strip,

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K factor nomograph: K = ƒ(5 soil properties)

(Troeh et (al. 2004)

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Multi-segmented slopes (2-5)

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D. RUSLE (Revised USLE 1992)

1. Improved mapping of R values in lower 48 & HawaiiHawaii

2. K & C allowed to vary seasonally by climatic datadata

3. C becomes a continuous function w/ 5 subfactorsa. Prior land useb. Surface coverc. Crop canopyp pyd. Surface roughnesse. Soil moisture

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4. Data gathered to develop local databases for C factors

5 P factor includes data from5. P factor includes data from

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II Oth i d lII. Other erosion models

A Empirical ModelsA. Empirical Models

1. RUSLE2: computerized extension of RUSLE

a. includes much more detailed information about slope, veg, residues, P factors, etc.

b. used to compare erosion under

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2. AGNPS: Agricultural Nonpoint Source Pollution ModelPollution Model

a. developed by USDA ARS to estimate ff t lit f AG t h drunoff water quality from AG watersheds

b. cell-based, distributed-parameter, event-driven model

c requires > input parametersc. requires > input parameters

d.

e. integrated with Arcview GIS interface &

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includes RUSLE subroutines

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3. EPIC: Erosion Productivity Impact Calculator

a. designed to assess effect of erosion on productivityp y

b. computes erosion from a single point on the landscapelandscape

c.

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B. Process-based models

1. WEPP: Water Erosion Prediction Project

b d di t ib t d ta. process-based, distributed parameter, continuous simulation, erosion prediction model

b. 1st model for erosion prediction in the U.S. not based on USLE

c. Based on equation:

Qs = sediment load per unit width per unit timex = distance downslopeDi = delivery rate of particles detached by interrill erosion

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Di delivery rate of particles detached by interrill erosionDf = rate of detachment/deposition by rill flow

Di = KiI2CeGe(Rs/w)

Di = interrill erosion rateKi = interrill erodibilityI =I =Ce = effect of plant canopyGe = effect of ground coverRs = spacing of rillsw = width of rills

Ce = 1 – Fe-0.34PH

Fe = fraction of soil protected by canopyPH =

Ge = e-2.5gi

gi = fraction of interrill surface covered by vegetation or residue

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Df = Dc(1-Qs/Tc)

Df = rate of detachment of soil particles by rill flowDc = detachment capacityQs = sediment load in the flowQs sediment load in the flowTc = sediment load at transport capacity

Dc = Kr(τ - τc)

Kr =τ = flow sheer stress acting on soilτ = critical flow sheer stress for detachment to occurτc critical flow sheer stress for detachment to occur

Tc = ktτ3/2

kt = is a transport coefficientτ = hydraulic shear acting on the soil

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d. When tested for 4,000 storm events across 9 i t l t ti i th U S WEPP9 experimental stations in the U.S., WEPP model gave predictions of mean annual soil loss at the plot scale of similar accuracy to ythose of USLE & RUSLE (Zhang et al. 1996)

e Web version:e. Web version:

http://milford.nserl.purdue.edu/wepp/weppV1.html

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2. European Soil Erosion Model (EUROSEM)

a. Funded by EU, developed by scientists in late 80s & early 90s

b. Modular structured, process-based model that incorporates terms of erodibility, roughness that p y, gchange w/ time

cc.

dd.

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(Morgan 2005)

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