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SOIL LOSS EQUATION & ESTIMATION

Dr. Abdul Gafur
Ex. CSO, SRDI, Dhaka

Soil Erosion refers to the gross amount of soil dislodged by raindrops, overland flow, wind, ice or
gravity, whereas Soil Loss indicates the net amount of soil moved off a particular field or area. The
conditions which influences soil loss through erosion and the preservative measures are illustrated as
follows.

Fig 1. Erosion
processes & preservative measures

Soil Loss Estimation

Several investigators have developed various predictive Soil Loss Estimation models. Eventually
Universal Soil Loss Equation (USLE) continues to be widely accepted method of estimating sediment
loss despite its simplification of many variables involved. It is useful for determining the adequacy of
conservation measures in farm planning, & for predicting nonpoint sediment losses in pollution control
programs. The average annual soil loss, as determined by Wischmeier & Smith (1978) can be estimated
from the equation:

A = R.K.L.S.C.P (Mg.ha-1.yr-1) In which,

A = average annual soil loss (Mg.ha-1 yr-1),

R = annual rainfall & runoff erosivity index for geographic location (MJ.mm.ha-1yr-1),
K = soil erodibilty factor (ton.ha.hr.ha-1.MJ-1.mm-1),
L = slope length factor,
S = slope gradient/steepness factor,
C = cover management factor,
P = conservation practice factor.
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Annual Natural
Physical
Human
Soil influence
Loss Conditions

A = R x K x L x S x C x P
Fig 2:
Different factors of Soil Loss Equation

Commonly used Equations & Calculations of USLE

1. Rainfall and Runoff Erosivity Index (R)

The rainfall and runoff factor (R) of the Universal Soil Loss Equation (USLE) was derived from
research data from many sources, and is generally recognized as one of the best indicator of the erosive
potentials of raindrop impact (Renard et al., 1991). The data indicate that when factors other than
rainfall are held constant, soil losses from cultivated fields are directly proportional to a rainstorm
parameter, i.e., the total storm energy (E) times the maximum 30-minutes rainfall intensity (I30). Rain
erosivity varies with the type of shower, characterized by the rain volume per rain intensity, duration of
high intensity rainfall and the drying spell between showers. The EI value of all the storms occurring in
a given year for a location are added to give an annual erosivity index.

EI30 method was introduced by Wischmeier is based on the fact that, the product of kinetic energy of the
storm and the 30-minute maximum rainfall intensity, gives the best estimates of soil loss. Highest 30-
minutes rainfall intensity (I30) can be computed from the data of the automatic rain gauge. By knowing
the maximum amount of rain in 30-minutes, the same is converted in the form of intensity (mm h -1),
simply by doubling the amount of I30.

After having the maximum rainfall intensity for 30-minutes durations, the kinetic energy of the
rainstorm can be computed in the metric-units using the unit energy relationship recommended by
Brown and Foster (1987) as:

Em = 0.29 [1-0.72 exp (-0.05 i)]

Where Em has units of MJ.ha-1.mm-1 of rain and i has units of mm.h-1.

The value of EI30 for a given rainstorm equals the product of total storm energy (Em) times the maximum
30-min intensity (I30) (Renard et al., 1997). The relationship followed to calculate the rainfall erosivity
R,

n
Rm=  ( EI30)im/N(m) (MJ.ha-1.yr-1)
I=1
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In which, R = yearly erosivity index in MJ.ha-1.mm.h-1, N = number of year period, n = number of storm
in year in an N year period, (EI30)i = EI30 for storm i in MJ.ha-1.mm.h-1, EI30 = Storm energy (E) * the
maximum 30 minute rainfall intensity in that storm (I 30), E = storm energy (MJ.ha-1), i.e., the sum of the
product of Em and rain depth.

Event-wise (rainfall) erosivity are computed and added together to get daily, weekly, monthly and yearly
erosivity values for any study period. All rainfall events (maximum one hour's of no rainfall) are
accounted for erosivity estimation irrespective of rainfall amount and intensity.

Monthly Erosivity Index (R), MJ.ha1.mm.hr-1. *

Months of the year
Year
April May Jun Jul Aug Sep Oct Nov Dec
2008 0.00 2576.40 6449.30 2542.2 2069.42 1465.54 1285.75 30.00 12.00
2009 279.60 7556.92 2882.17 1119.1 4138.71 2927.44 90.37 28.00 -
* Data generated at the SCWMC, SRDI, Bandarban.

2. Soil Erodibilty Factor (K)

Soil Erodibility (K) is closely related to various soil properties by which a soil becomes susceptible to
get erode, either by water or wind. Physical characteristics of the soil greatly influence the rate at which
different soils are eroded. Soil properties like soil permeability, infiltration rate, soil texture, size &
stability of soil structure, organic matter content & soil depth also affects the soil loss in large extent.
Soil Erodibility Factor (K) is expressed as tones of soil loss per hectare per unit rainfall erosivity index,
from a field of 9% slope & 22 meters as field length. This is determined by considering the soil loss
from continuous fallow land without the influence of crop cover or management.

As soil loss data are not always available, K values have been approximates by using soil analytical data
and the Soil Erodibility Nomograph (Fig 3).

The percentage of clay content in the soil is assumed as an indicator of soil erodibility. Theoretically, the
following points can justify it:
* The clay particles are combined with the organic matters and formed soil aggregates or clods,
which provide greater resistance to reduce the erosion.
* Soils containing high content of base minerals are found more stable, as these materials
contribute chemical binding to the aggregates.
* The soil moisture has great effect on soil erodibility.

When soil is wetted, the aggregates are weakened, because the cementing substances which make the
soil cohesiveness, becomes dispersed throughout the aggregates, as a result the resistance to erosion gets
reduced. Apart from this particular effect of moisture content on soil resistance or erodibility, the
wetting of soil also causes swelling of clay particles, which also affects the soil erodibility.

Bouyoucos (1935) suggested that, the soil erodibility depends on mechanical composition of soil, such
as sand, silt, and clay. It is presented in the ratio, given as:

Erodibility E = g (% Sand + % Silt)/ % Clay

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Data on Erodibilty Index (K) (Data generated at the SCWMC, SRDI, Bandarban)

Plots Description p s OM M K=1/759.4[2.1*10-4*(12-OM)

M1.14+3.25(s-2)+2.5(p-3)]
Gentle slope with Jhum 4 4 3.778 1800.47 0.02354
cultivation (GJ)
Moderate slope with 4 4 3.729 2172.91 0.02642
Jhum cultivation (MJ)
Steep slope with Jhum 4 4 3.756 2324.04 0.02753
cultivation (SJ)

Where, OM = organic matter (%),

M = primary particle size fraction (%silt +%vf sand)*(100 - % C); [Diameter of
C= < 0.002 mm, Si= 0.002-0.006 mm, S= 0.006-2 mm]
s = code for soil structure (very fine granular, 1; fine granular, 2; medium or
coarse granular, 3; blocky, platy, or massive, 4), and
p = code for profile permeability class (rapid, 1; moderate to rapid, 2; moderate,
3; slow to moderate, 4; slow, 5; very slow, 6).

3. Slope Length and Slope Gradient Factor (LS)

The effect of topographic factors on erosion is accounted for by the Slope Length (L) and Slope
Gradient (S) factors. Erosion increases as slope length increases, and is considered by the slope length
factor. Slope length is defined as the horizontal distance from the origin of overland flow to the point
where either the slope gradient decreases enough that deposition begins or runoff becomes concentrated
in a defined channel (Wischmeier and Smith, 1978). In USLE, the factors taken into account are;
differences between very short (<5m) and longer slope length, rill sensitivity of soils and slopes, effect
of freezing, slope shape as complex slope profiles. Plot data used to derive the slope length factor have
shown that average erosion for the slope length varies as:

L = (x/22.13) m

In which L= slope length factor,

x = slope length (meter),
m = dimensionless slope length exponent.
Slope length x, is the horizontal projection not the distance parallel to the soil surface.

Slope gradient is the field or segment slope, usually expressed as %. Wischmeier (1958) observed that
soil loss was correlated with a parabolic description of the effect of slope gradient.

The slope length exponent m is related to the ratio  of rill erosion (caused by flow) to interrill erosion
(principally caused by raindrop impact) by the following equation (Foster et al 1977)
m = / (1+) where  = ratio of rill to interrill erosion.
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Values of  for the conditions when the soil is moderately susceptible to both rill and interrill erosion are
computed from (McCool et al, 1989)

= (sin/ 0.0896)/3.0(sin)0.8 +0.56 -

In which,  (degree) is the slope angle.

Slope Steepness Factor S:

The slope steepness factor (S) reflects the influence of slope gradient on erosion. Soil loss increases
more rapidly with slope steepnss than it does with slope length.In RUSLE the slope steepness factor is
evaluated from (McCool et al, 1987) :

S = 10.8 sin +0.03 for s< 9%; S = 16.8 sin -0.05 for s 9%
In which, S =Slope steepness factor -, s =Slope steepness %,  =Slope angle (degrees).

The author of USLE recommended that the factors of slope length & slope gradient be used in
combination, i.e., as the combined LS factor for which they recommended the equation:

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

Where, LS = Slope length & slope gradient factor

x = Slope length (m),
s = Slope gradient, % and
m = an exponent

They also recommended the values of

m = 0.5, if slope is  5 percent
m = 0.4, if slope is < 5% and > 3%
m = 0.3, if slope is  3% and  1% , and
m = 0.2, if slope is < 1 percent

Slope Length Factor (L)

Plots Slope Slope =(sin/0.0896)/ m=(/1+) Slope L=(/65.62)

Description % Angle  [3(sin)0.8+0.56] length  m

Plot, GJ 15% 8.53 1.366 0.577 19.78 0.50

Plot, MJ 23% 12.95 1.705 0.630 19.49 0.465
Plot, SJ 46% 24.70 2.2.72 0.694 18.17 0.410
GJ: Gentle slope with Jhum cultivation
MJ: Moderate slope with Jhum cultivation
SJ: Steep slope with Jhum cultivation

Slope Steepness Factor (S)

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Plots Description Slope % Slope Angle,  S=(sin/0.0896)0.6

Plot, GJ 15% 8.53 1.353
Plot, MJ 23% 12.95 1.733
Plot, SJ 46% 24.70 2.52
GJ: Gentle slope with Jhum cultivation
MJ: Moderate slope with Jhum cultivation
SJ: Steep slope with Jhum cultivation

LS computed from the above equations can be easily read from Chart (Fig 4) using slope in % & slope
length in meters.

Cover Management Factor ©

Cover management factor (C) may be defined as the expected ratio of soil loss from a cropped land
under specific crop to the soil loss from a continuous fallow land, provided that the soil type, slope and
rainfall conditions are identical. C factor includes the effect of cover, quality of cover, root growth,
water use by growing crop, crop sequence, productivity level, length of growing season, tillage practice,
residue management & expected time distribution of erosion events. These features differ variously
within the period from planting to the crop harvesting & accordingly the soil loss also gets affected.
Similarly, the variation in rainfall distribution within the year also affects the crop management factor,
which affects soil loss. Many state agencies have developed C factor tables for their respective climate
pattern and cropping practices to aid field staff in working with the USLE.

Conservation Support Practices (P)

Conservation support practice refers to the practices of plant management, cultivation system, land
management and small construction works for reducing soil losses. According to soil conservation
society of America soil conservation is part of conservation of the land: the protection improvement and
use of natural resources according to principles that will assure their highest economic or social benefits
for man and his environment now and to the future.

The conservation practice P can be found from the equation:

P = Pc + Ps + Pt

Where Pc = contouring factor based on slope

Ps = strip cropping factor for crop strip widths recommended as, 1 for contouring
only or for alternate strips of corn and small grain, 0.75 for 4-year rotation
with 2 years of row crop, and 0.50 with 1 year of row crop.
Pt = terrace sedimentation factor (1.0 for no terraces, 0.2 for terraces with graded
channel sod outlets, and 0.1 for terraces with underground outlets.
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Conservation support practice factor, P of the USLE, is the ratio of soil loss with a specific support
practice to the corresponding loss with upslope and down slope tillage. These practices principally affect
erosion by modifying the flow pattern, grade or direction of surface runoff and by reducing the rate and
amount of runoff. Strip cropping is a support practice where strips of cleaned tilled or nearly cleaned
tilled crops are alternated with strips of closely growing vegetation such as grasses, legumes etc.
Densely vegetated strips or very rough strips that produce deposition of eroded sediment are assigned a
P-factor value. A strip is effective in reducing soil loss when it significantly reduces the transport
capacity of the runoff as it leaves one strip and enters the next strip. For deposition to occur, the
transport capacity must be reduced to less than the sediment load being transported by the runoff. If no
deposition occurs, the value is 1.0.

Some typical conservation practices values (p) are given in Table

Land Slope (%) Contour Ploughing Strip Cropping

0-7 0.50 0.25
8-12 0.60 0.30
13-18 0.80 0.40
19-24 0.90 0.45

Soil erosion studies are usually carried out on field plots (small; medium; large) to predict & evaluate
soil erosion & sediment yield. Small plots studies are mostly complementary to field plot experiments.
On the contrary large plots are small watersheds big enough to accommodate at least one natural
drainage way. A major disadvantage in the watershed research is that the generated data of one
watershed are difficult to apply to other watersheds.By applying these equation the average annual soil
loss can be computed for any region; but before doing so, its validity should be clarified.

Estimated Soil Loss using USLE from an Experimental Plot at SCWMC, Bandarban

Month May-08 Jun-08 Jul-08 Aug-08 Sep-08 Oct-08 Nov-08 Dec-08

Factor
R(MJ.ha- 2576.40 6449.30 2542.2 2069.42 1465.54 1285.75 1.46 30.00
1
.mm.hr-1)
K(t.hr.MJ- 0.02753 0.02753 0.02753 0.02753 0.02753 0.02753 0.02753 0.02753
1
.mm-1)

L [-] 0.410 0.410 0.410 0.410 0.410 0.410 0.410 0.410

S [-] 2.520 2.520 2.520 2.520 2.520 2.520 2.520 2.520
C [-] 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20
P [-] 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55
Monthly 8.608 20.176 7.952 6.472 4.584 4.016 0.00456 0.0936
Total Soil
Loss (t.ha-1)
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Conversion Tables for Natural Tangent to Degrees

Slope Data Ratio Degrees Slope
Percent Slope Degrees & (tan)* (rounded) (%)
Minutes 1:0.25 76 400
1 0o34’ 1:0.5 63
5 2o52’ 1:1 45 100
10 5o43’ 1:1.5 34
o
15 8 32’ 1:2 27 50
o
20 11 19’ 1:2.5 22
o
25 14 02’ 1:3 18 35
o
30 16 42’ 1:3.5 16
35 19o45’ 1:4 14 25
40 o
41 48’ * First figure refers to the height,
45 24o14’ 2nd to the horizontal distance; eg
50 26o34’ on a 1:2 smooth slope there is a
60 30o38’ climb (or decent) of 5m for every
70 35o00’ 10 m traversed horizontally along
80 38o40’ a line parallel to the maximum
90 42o00’ gradient
100 45o00’
200 63o50’
300 71o57’
500 78o59’ 1 in 2 Slope
5
1000 m 84o30’

2000 87o15’ 10 m
5000 88o36’
10000 89o43’ 27o rounded,
50% Slope

Percentage Slope = Natural Tangent * 100; thus 1:2 = 50%