Transcript No Slide Title

MODELLING OF SOIL EROSION
Purpose
• research tool
• sensitivity analysis during planning
• design of engineering works
USLE
Developed from 15,000 plot years in USA:
Standardised plots : 9% slope, 72.6 ft long
A=RKLSCP
[A is mean annual soil loss in t/ac/yr]
Rainfall
R = rainfall factor = erosivity/100
Erosivity EI30
= kinetic energy x maximum 30 minute
intensity
(but this parameter is a simplification
of what is going on & may not be
applicable in some instances)
Monthly and annual EI30 are calculated
by summation of individual storms.
Definition of a storm:
• average intensity must be > 0.25 mm/hr
• must be separated by > 2 hrs from last rain
(otherwise counted as same storm)
• at least one 5 minute with > 25 mm/hr
• > 12.5 mm total.
To calculate EI30 from first principles, drop size
distribution. v. intensity required.
Therefore, equations such as the following have
been derived to eliminate need for drop size assumes relationship between drop size and
intensity:
logarithmic relationship -
E  11.87  8.73log10 I (J/m2 / mm) [for USA- Wischmeier & Smith,1958]
reciprocal relationship
E  29.8 127.5 / I (J/m2 / mm) [for Zimbabwe - Hudson,1965]
Note these are per mm of rain.
For a whole year sum EI30 for each storm.
Other people have looked for regional equations to find
relationships between :
• Es & I(t) throughout the storm
• Es & R (and sometimes I30)
• EsI30 to Rs (and sometimes I30)
R » 0.5 x annual rainfall in tropics [approx.]
where R, the rainfall erosivity index, is the
average yearly total of EI30 / 100 in ft-ton/acre
and rainfall in mm.
See handout for equations for predicting rain erosivity.
Handouts
More precisely for Kenya:
R = 0.29 Ey - 26
[in British units where R is the rainfall erosivity
index and Ey is the annual kinetic energy of the
raindrops] 1
Another source2 gives (again for Kenya):
Ey = 22P - 15795 (in metric units where
here P is the annual rainfall amount in
mm)
1Soil
Cons. in Kenya?
2Soil conservation for agroforestry?
Example (from Morgan, p. 47)
Time from start (min)
Rainfall
(mm)
Intensity (mm h-1)
Kinetic energy per unit of
rain (J m-2 mm-1)
0-14
15-29
30-44
45-59
60-74
75-89
1.52
14.22
26.16
31.5
8.38
0.25
6.08
56.88
104.64
126.00
33.52
1.00
8.83
27.56
28.58
28.79
26.00
-
Total kinetic energy per time
slice (col 2 x col 4)
[J m-2]
13.42
391.90
747.65
906.89
217.88
-
Energy per mm of rain calculated from:
E = 29.8 - 127.5/I (for Zimbabwe - see above)
Maximum 30 minute rainfall = 26.16 + 31.5 = 57.66
Maximum 30 minute intensity = 57.66 x 2 = 115.32 mm h-1
Total kinetic energy = 2277.74 J m-2 [total of column 5]
EI30 = 2277.74 x 115.32 = 262669 J m-2 mm h-1
Hudson index of erosivity (KE>25) - energy for rain over
25 mm h-1
= rows 2, 3, 4 & 5 of column 5 = 2264 J m-2 mm h-1
Other factors in USLA
Erodibility
K = soil erodibility factor (mean annual soil loss per
unit of erosivity)
defined such that K is erosion rate relative to that
from a standard plot 22 m long & 9% slope with no
conservation practices.
Examples shown overleaf
Length & degree of slope
L = slope length factor
[relative to loss from 22m]
S = slope steepness factor
[relative to loss from 9%]
L & S factors are usually combined into a LS factor.
One of the earliest equations was due to Zingg (1940):
A = C S1.4 L0.6
where
A was the average soil loss per unit of AREA ,
C was a constant,
S was land slope (%),
L was slope length (ft).
Soil loss per unit WIDTH of slope would be
A = C S1.4 L1.6
In Wischmeier & Smith (no relation) equation:
“LS” = (l 0.5/22.13) x (0.065 + 0.045s + 0.0065s²)
Note that this factor relates to the soil loss per
unit area.
For soil loss per unit WIDTH, the exponent would
be 1.5.
Cover and management factor
C = cover and management factor [relative to bare fallow]
e.g.
C = 0.8 for maize or tobacco
C = 0.01 for well managed tea
C = 0.001 for natural rain forest
other values in table following
To arrive at an annual factor, the variation of crop
morphology throughout the year needs to be taken into
account. Ground cover such as stubble between the
cropping seasons is also allowed for.
Can be divided into three parts : C-I -
for plant canopy cover (for a given %
cover, taller crops have a higher C-I)
C-II -
% of soil surface covered by mulch
C-III - root network from previously
undisturbed land
In RUSLE,
C = PLU . CC . SC . SR
where
PLU is a previous land use factor,
CC is a crop canopy factor,
SC is surface or ground cover factor and
SR is a surface roughness factor
Practice factor
P = practice factor [relative to erosion from field
with plant rows up/down slope].
If neither contouring nor strip cropping practised
and no other conservation measures, the value is
1.0
e.g. P = 0.4 for strip cropping
P = 0.05 to 0.1 for well maintained terraces
USLE needs modifying and calibration for use in
the tropics. This has been done for some
countries such as India, Ethiopia
USLA adapted for Ethiopia
Adaptations:
R correlation based on Hurni, 1985
K values from Bono and Seiler, 1983, 1984 and Weigel, 1985
S extrapolation based on Hurni, 1982
Equation: A = R x K x L x S x C x P
1. Rainfall erosivity
Annual rainfall (mm) 100
200
400
800
1200
Annual R factor
48
104
217
441
666
2. Soil erodibility
Soil colour
black
brown
red
yellow
K factor
0.15
0.2
0.25
0.3
3. Slope length
Length (m)
5
10
20
40
80
L factor
0.5
0.7
1.0
1.4
1.9
4. Slope gradient
Slope (%)
5
10
15
20
30
S factor
0.4
1.0
1.6
2.2
3.0
5. Land cover, C
1600
890
2000
1115
2400
1340
160
2.7
240
3.2
320
3.8
40
3.8
50
4.3
60
4.8
Dense forest
Sparse forest
Dense grass
Degraded grass
Badlands - hard
Badlands - soft
0.001
see grass
0.01
0.05
0.05
0.4
Fallow - hard
Fallow - ploughed
Sorghum or maize
Cereals, pulses
Teff
Cont. fallow
0.1
0.15
0.25
1
0.05
0.6
6. P, management factor
Ploughing up & down
Ploughing on contour
Stone cover = 40%
Stone cover 80%
1.00
0.9
0.8
0.5
Applying mulch
Strip cropping
Intercropping
Dense intercropping
0.6
0.6
0.8
0.7
Example of the effect of ground cover
2% slope at Nyankapa, Nigeria3
Treatment
Bare fallow
Groundnut cover
Mulching
Ridging
Minimum tillage
Mixed cropping
Soil loss
(t ha-1)
1.83
0.18
0.089
0.19
0.19
0.31
C factor
100
9.8
4.9
10.4
10.4
16.9
mm
7.9
3.07
1.22
0.7
1.41
4.04
Runoff
% runoff
3.1
1.2
0.48
0.27
0.55
1.59
Bare fallow was the control
Groundnut cover was an intercrop
3Bonsu.
1980. Erosion & cultural practices. In Morgan, 1980. p. 251
Millet yield
470 -750
1130 - 1275
1182 - 1350
680 - 700
560
SLEMSA (Soil Loss Estimation Model for South
Africa)
Z = KCX t/ha/yr
where: K = soil loss from 30 m plot @ 4% == f(rain
energy, soil)
C = crop factor = f(energy intercepted)
C = 0.3 if 0.2 energy intercepted
C = 0.1 if 0.4 energy intercepted
C = 0.05 if 0.5 energy intercepted
X = topographic factor = f(slope angle, length)
= LS of Wischmeier & Smith, approximately
FAO
This a simplified version of the USLE used by the
FAO:
A = RKSC (ignores length & management)
•
designed for large scale mapping of relative
potential erosion
Musgrave type erosion
Some experiments on unrilled slopes show a rapid
increase (over a few metres) of sediment load
carried by overland flow to a capacity which remains
relatively constant regardless of slope length. The
basic equation is:
y  kq s
m n
where
y is the sediment yield, q the overland flow and
s the slope angle
Morgan (1980) gives:
y  kq s
2 1.66
Others
• Hairsine-Rose model
• Rose model [- both complex mathematical models
for detachment, entrainment, and deposition]
• CREAMS (Chemicals, Runoff, and erosion from
agricultural management systems)
• EPIC (Erosion Productivity Impact Calculator)
• SCUAF (Soil changes under agroforestry)
• RUSLE (Revised Universal Soil Loss Equation) see Hudson, 1995 for summary of changes
• WEPP (Water Erosion Prediction Project;
theoretical analysis; meant to replace USLE see
Chapter 5 in Morgan; also Hudson, 1995
• Stehlík (for Czech Rep. & Slovakia)
Indices of soil erodibility
See Table 1 Handout
It gives various methods of comparing soil
erodibility.
Apart from the K value of Wischmeier and Smith,
these cannot be used in the USLE directly.
They would need to be calibrated and
related to K.
Estimates of K from soil properties
A method of estimating K from soil properties is
given in Figure 1.
You need estimates of
•
•
•
•
•
organic matter content
percentage sand (0.1 to 2 mm)
percentage of silt to very fine sand
soil structure
permeability
Starting with the percentage of silt + v. fine sand,
enter the diagram on the left vertical axis. Continue
horizontally until you meet the percent sand curves
(running from top left to bottom right) and stop
when you reach the curve corresponding to the
sample's value for sand. Then go vertically until you
reach the Organic Matter (OM) group of curves and
stop when you reach the sample's OM value. Then go
horizontally into the second diagram and stop when
you reach the soil structure curves. Proceed
downward until you reach the permeability curves
and stop when you intersect the curves estimated
permeability. Then turn horizontally going left until
you reach the vertical axis of K. Read off the value.
The example shown is for a soil having
• silt + v. fine sand = 65%
• sand = 5%
• OM = 2.8%
• structure = fine granular
• permeability = slow to moderate
Where the silt fraction does not exceed 70 percent, the
equation is
100 K = 2.1 M1.18 (104) (12 - a) + 3.25 (b - 2) + 2.5 (c - 3)
where
M = (percent si + vfs) (100-percent c),
a = percent organic matter,
b = structure code
c = permeability class
Nomograph for estimating soil
erodibility (K) based on soil
properties. From Morgan, p. 54,
quoting Wischmeier, Johnson and
Cross, 1971.