What makes the The Universal Soil Loss Equation

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• What makes the The Universal Soil Loss Equation
• Go ?

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Universal Soil Loss Equation

• Erosion f (climate, soil, topography,
  landuse) A R K
  LS C P
• A average annual erosion in field sized
  areas
• R rainfall-runoff (erosivity) factor
• K soil (erodibility) factor
• LS topographic factors (L re slope length
  S re slope gradient)
• C crop/crop management factor
• P soil conservation practice factor

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Universal Soil Loss Equation

• Erosion f (climate, soil, topography,
  landuse) A R K
  LS C P
• C, P L are the main factors modified by
• land management

Erosion has units of weight per unit area (t/ha)
- the weight is an average value over that area
but that dose NOT mean that erosion is
uniform over that area.
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Universal Soil Loss Equation

• Erosion f (climate, soil, topography,
  landuse) A R K
  LS C P
• The Revised USLE (RUSLE)1997
• An update of the USLE to take account of new
  information gained since the 1960s and 70s
• USLE/RUSLE used widely in the world

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Based on Erosion from PlotsKey issue Unit
Plot

• 22 m long
• 9 slope gradient
• Bare fallow (no vegetation), cultivationup and
  down slope
  
• 
  L S C P 1.0

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Unit Plot 22m long 9 slope
Wheat Plot 33m long 6 slope

• ? A1 R K10 t/ha
• ? AC A1 ( L S C P )
• ? AC 10 (1.22 x 0.57 x 0.16 x 1.0)
  1.1
  t/ha
• L, S, C and P are all ratios with respect to unit
  plot conditions
• The model operates in two stages - predicts A1
  then AC

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R rainfall-runoff factor

• N N number
  of events in Y years ? Re
  Re Event erosivity factor
  e1 R
  Y Y number of years

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Event Erosivity

• Re E I30 E Event
  Energy I30 max
  30 min intensity

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K soil erodibility factor

• N
  N number of events
• ? Ae.1
  Ae.1 loss for CPLS1
• e1 (5 years of data)
• K
• N C1 bare fallow
  
• ? (EI30)e L1 22.13
  m
• e1 S 1 9 slope
  P1
  cult up/down slope

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K soil erodibility factor

• K from field experiments
• Time - 5 years or more
• Expense - setup of plots (equipment and labour)
  - maintenance (equipment and labour)
  - resources tied up in data
  collection
• Predict K from soil properties
  - less time and expense

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K from soil characteristics

• K 2.77 M1.14 (10-7) (12-OM) 4.28 (10-3)(SS-2)
  3.29(10-3) (PP-3)
• Developed by Wischmeier el al (1971)
• for soils where silt very fine sand is 70 and
  less
• K in SI units
• M ( silt very fine sand) (100 - clay)
  - soil texture
• OM organic matter
• SS soil structure code (USDA Soil Survey Manual)
• PP profile permeability class (USDA Soil Survey
  Manual)
• Other equations exist for other soils (Volcanic)
  and using other properties

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Seasonal variation in K

• In RUSLE, K can be considered to vary during year
  in association with soil moisture
• In USA wet in spring gtgtgt dry during
  summercausing K to fall spring gtgtgt summer
• Not necessarily appropriate in all geographic
  locations

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L slope length factor
L (? / 22.13) m

• USLE m0.6 slope gt10 ? m0.2 slope
  lt1
• RUSLEm ? / (1?) ? ratio rill to
  interrill erosion
• ? depends on soil and slope

• is the projected horizontal distance travelled
  by runoff before deposition or a channel occurs

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Erosion for non-uniform slopes
L applies to uniform slopes

• How is it used to calculate erosion for non
  uniform slopes ?

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Erosion for non-uniform slopes

• Uniform slope gradient different crops

Non-uniform slope gradient same or different
crops
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Erosion for non-uniform slopes
Can only calculate L for lengths starting at the
top of the hillslope

• Calculate L for ? (?/22.13)m
  (Lslope)
• Calculate L for ?1 (?1/22.13)m
  (L1)
• Multiply Lslope by ? subtract L1 by ?1 (X)
• Divide X by ?2 L for lower segment

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Erosion for non-uniform slopes

• Reverse of calculating the average for whole
  slope (L1 x ?1) (L2 x ?2)
  Lslope
  
  ?

• Calculate L for ? (?/22.13)m
  (Lslope)
• Calculate L for ?1 (?1/22.13)m
  (L1)
• Multiply Lslope by ? subtract L1 by ?1 (X)
• Divide X by ?2 L for lower segment

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Erosion for non-uniform slopes

• Reverse of calculating the average for whole
  slope Lslope x ? (L1 x ?1) (L2 x ?2)
  

• Calculate L for ? (?/22.13)m
  (Lslope)
• Calculate L for ?1 (?1/22.13)m
  (L1)
• Multiply Lslope by ? subtract L1 by ?1 (X)
• Divide X by ?2 L for lower segment

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Erosion for non-uniform slopes

• Reverse of calculating the average for whole
  slope Lslope x ? - (L1 x ?1) (L2 x ?2)
  

• Calculate L for ? (?/22.13)m
  (Lslope)
• Calculate L for ?1 (?1/22.13)m
  (L1)
• Multiply Lslope by ? subtract L1 by ?1 (X)
• Divide X by ?2 L for lower segment

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Erosion for non-uniform slopes

• Reverse of calculating the average for whole
  slope (Lslope x ? - (L1 x ?1) ) / ?2
  L2

• Calculate L for ? (?/22.13)m
  (Lslope)
• Calculate L for ?1 (?1/22.13)m
  (L1)
• Multiply Lslope by ? subtract L1 by ?1 (X)
• Divide X by ?2 L for lower segment

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Erosion for non-uniform slopes

• Lslope (? /22.13)m where ? distance to
  bottom of segment (Lslope x ? - (L1 x
  ?1) ) / ?2 Lseg

L for a segment increases downslope and so does
erosion
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Erosion for non-uniform slopes
Calculation method the same as for uniform slope
gradient because m is determined only the
gradient of the 2nd segment
Seg 1 has different slope

• Calculate L for ? (?/22.13)m (Lall)
• Calculate L for ?1 (?1/22.13)m
  (L1)
• Multiply Lall by ? subtract L1 by ?1 (X)
• Divide X by ?2 L for lower segment

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Erosion for non-uniform slopes

• Crops are irrelevant to calculation of Lseg
• But are relevant in the calculation of segment
  and hillslope erosion
• A1 R K L1 S1 C1 P1A2 R K L2 S2 C2 P2
• (A1 x ?1) (A2 x ?2) Aslope
  
  ?

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Potential Real Erosion
For a hillslope (A1 x ?1)
(A2 x ?2) Aslope
?Only valid
if no deposition in lower segment

• RUSLE 2 does deals with deposition
  using transport capacity
  (TC) concept
• A1 5 t/ha A2 1t/ha
  both segs are 1ha in area
  TC2 4t
• Seg 1 produces 5t. 4t passes through to the
  bottom of seg 2. 1t deposited in seg 2 and no
  erosion occurs in seg 2.
• Hillslope has lost 4t of soil because of the
  control by seg 2.

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Potential Real Erosion

• The USLE predicts potential erosion
• Deposition will result in real erosion differing
  from what USLE predicts
• The ratio of Real Erosion to Predicted Erosionis
  the Delivery Ratio

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RUSLE 2

• Wheat on 18m at 10, 18m at 6, 9m at 2
• Slope delivery
• 3.8 T/A
• Soil loss
• 7.7 T/A
• Delivery Ratio
• 0.49

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Sediment Delivery Ratio

• Varies with catchment size
• But large variation about the SDR - size
  relationship depending on catchment
  characteristics
• In case of SDR from RUSLE 2 data,SDR modelled
  erosion to modelled sediment delivery based on a
  sediment transport model

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S slope factor

• USLES 65.4 sin2 ? 4.56 sin ? 0.0654
  ? angle to horizontal
• RUSLES 10 sin ? 0.03 slopes
  lt9S 16.8 sin ? - 0.50 slopes ?9
  USLE S overpredicts erosion at high slope
  gradients

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C crop management factor

• N
  ? Ae.C e1 C
  N ? Ae.1
  e1 Ae.C event loss with
  cropAe.1 event loss for bare fallow

• N
  ? Ae.C e1 C
  
• N K ? (EI30)e
  e1
• C varies geographically

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C varies geographically

• C for WheatZone C 5
  0.20 6 0.14
  7 0.15 8 0.15
  9 0.15 10
  0.16 11 0.29 12
  0.14

Australia New South Wales has 12 Climate Zones
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C varies geographically

• C for WheatZone C 5
  0.20 6 0.14
  7 0.15 8 0.15
  9 0.15 10
  0.16 11 0.29 12
  0.14

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C varies geographically

• C for WheatZone C 5
  0.20 6 0.14
  7 0.15 8 0.15
  9 0.15 10
  0.16 11 0.29 12
  0.14

1.8x
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C varies geographically

• Zone 11 has grater proportion of R during
  cultivation period
• Zone 11 not good for growing wheat - less cover

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Calculating C

• C can be calculated by weighting the short term
  value of C (soil loss ratio) by the proportion of
  R in the period
• ? Ci Ri C
  _______________ ? Ci (Ri/R)
  R Ci C during period i
  Ri R during period i
• Normally 2 week periods

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Calculating C

• The soil loss ratio may, in turn, be calculated
  from subfactors accounting for prior land use,
  crop cover, surface (ground) cover, surface
  roughness
• Crop cover factor includes consideration of plant
  structure and height

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P support practice factor

• Accounts for impact of conservation practice
• eg. cultivation across slope vs up/down
  slopeP1.0 for cultivation up/downP0.5
  for cultivation across
• Support practicesAcross slope - P varies with
  ridge height, furrow grade Strip Cropping,
  Buffer strips, Filter strips, Subsurface drains

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Universal Soil Loss Equation

• Erosion f (climate, soil, topography,
  landuse) A R K
  LS C P
• Uses/Misuses
• Designed for looking at average annual erosion in
  field sized areas
• Help make management decisions
• Not for predicting erosion by individual events
  or seasonal or year by year variations in erosion

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• Peter Kinnell
• University of Canberra
• Canberra ACT 2601
• Australia
• peter.kinnell_at_canberra.edu.au