Universal Soil Loss Equation | Soil Management

In this article we will discuss about universal soil loss equation used to estimate soil loss.

The water erosion is a complex process. It involves inter-relationships between several factors. Few of them influence the potential of rainfall and runoff to detach and transport the soil particles from soil mass. And few are that, which affect the soil ability to resist the forces of erosive agents. On 40-years research by the USDA, it had come to identify the major factors involved in soil erosion; and to establish the functional relationships amongst them.

The data collected under various studies were based on standard runoff plots, often called ‘Wischmeier’ plots. The dimension of study plot was 22.13 m in length with 9% slope, in continuous fallow condition. More than 250,000 runoff events at 48 research stations in 26 states during 40-years were taken into consideration to collect the data for development of the Universal Soil Loss Equation (USLE) by Wischmeier and Meyer; and the same was published in the year 1973 by the Wischmeier and Meyer.

This equation was designated as Universal Soil Loss Equation; and in brief it is now as USLE. Since, then the USLE is in use, worldwide. It has been widely accepted and utilized in most the countries. It is a very simple and powerful tool for predicting the average annual soil loss in specific situations. The associated’ factors of the equation can be predicted by easily available meteorological and soils data.

The term ‘universal’ refers consideration of all possible factors affecting the soil erosion/soil loss; and also its general applicability. However, the USLE was designed for soil and climatic conditions within the U.S. But by small modification it can also be applied for special conditions (volcanic soils, tropical rains).

Recently, the USLE has been revised, and becomes more versatile and is more accurate representative of seasonal changes. The new version of USLE is referred to the Revised Universal Soil-Loss Equation or RUSLE, which was released for distribution in the year 1993.

The RUSLE maintains the general empirical-lumped model approach of USLE; and it is relatively easy to use with a minimum training. Recently, the process-oriented model, i.e. the Water Erosion Prediction Project or WEPP model has also been developed, is the substitute of RUSLE. The WEPP offers the ability to accurately predict the erosion and runoff for specific conditions, at the cost of requiring many more measured input conditions.

The USLE is given as under –

A = R K LS C P … (21.3)

Where,

A = computed soil loss, expressed in t/ha/y for a given storm event.

R = rainfall erosivity factor, which is the measurement of the kinetic energy of a specific rain event or an average year’s rainfall.

K = soil credibility factor. It is the soil loss rate per erosion index unit for a given soil as measured on a unit plot (22.1 m long with 9% slope in continuous clean-tilled fallow).

L = slope length factor. It is the ratio of soil loss from the field plot under existing slope length to that from the 22.1 m slope length (unit plot) under identical conditions.

S = slope gradient factor. It is the ratio of soil loss from the field slope gradient to that from the 9% slope (unit plot) under identical conditions.

C = cover or crop rotation (management) factor. It is the ratio of soil loss from the area under specified cover and management to that from an identical area in tilled continuous fallow (unit plot).

P = erosion control practices or soil conservation practices factor. It is the ratio of soil loss under a support practice like contouring, strip cropping or terracing to that under straight-row farming up and down the slope.

The USLE focuses the yield of soil erosion from a freshly tilled soil without cover or residue on 9% slope and 22.1 m long. Amongst several factors involved in USLE, the rainfall erosivity (R) and soil erodibility factor (K) determine the potential soil erosion form a given field plot under standard conditions.

While the other factors such as slope length factor (LS), crop management practices factor (C) and soil conservation practices factors (P) determine the possible reductions (or increase with slope) in quantum of soil erosion.

Rainfall Erosivity Factor (R):

It refers to the rainfall erosivity index, which expresses the ability of rainfall to erode the soil particles from an unprotected field. It is a numerical value. From a long term field studies, it has been observed that the extent of soil loss from a barren field is directly proportional to the product of two rainfall characteristics – (1) Kinetic energy of the storm; and (2) Its 30-minute maximum intensity.

The product of these two storm characteristics shows an interaction between the rainfall and run-off to dislodge the soil particles; and consequently to transport them away from the field. The product of kinetic energy and 30-minute maximum rainfall intensity is termed as EI or rainfall erosivity index.

The factor-R is the rainfall and runoff based factor was derived on the basis of research data from a large number of locations. The studies indicate that, when factors other than the rainfall are kept constant, then the soil losses from cultivated fields are directly proportional to the rainfall energy (KE) times the maximum 30-min rainfall intensity (I₃₀). The attempt should always made to compute the value of factor R for a specific rainfall event, more accurately for better accuracy in soil erosion estimation. The formula of factor-R is given by –

in which, E is the K.E. of rain event; I₃₀ is the rainfall intensity for maximum 30 minutes duration and n is the total number of rain events during a year.

The computation of factor-R is described as below:

Using Rain Events:

Lal (1988), Morgan (1986) and Renard et al. (1992) suggested that for a given rainfall event the rainfall factor (E.I₃₀) is the product of the total kinetic energy (E) of the rainfall event and its maximum 30-minute intensity (I₃₀). The median raindrop size generally gets increase with the rain intensity and terminal velocity of free falling raindrops.

The terminal velocity of raindrop gets increase with increase in drop size. Since, the energy of a given mass in motion is proportional to the velocity squared, therefore, the rainfall energy is directly related to the rain intensity.

The kinetic energy of rainfall event is computed from the recorded rain chart (mass curve) produced by the recording type rain gauge. The mass curve is sub-divided into specific intensity range or time interval. There have been developed several methods for computing the rainfall erosivity.

Here, a different method described by Morgan (1986) and Renard et al. (1992) is outlined as under:

In this method, the rain events producing 12.5 mm rainfall depth unless more than 6 mm in 15 minutes duration are counted for computation.

The steps are mentioned below:

i. Divide the rainstorm into 15-minute intervals.

ii. Determine the amount of rainfall for each interval.

iii. Compute the rainfall intensity in mm/h for each interval (I₁₅).

iv. Calculate the KE for each interval using the following equation.

In which, I₁₅ is the 15-minute rainfall intensity (mm/h); E_j is the kinetic energy (J mm^–1 m^–2) for interval j (1, 2, .., n) of the rainstorm. The limit of 76 mm/h is because of the reason that the median drop size does not increase when intensities exceed this.

i. Compute the total KE of each interval by multiplying KE and l₁₅ of respective interval; and adding together for getting total storm (E).

ii. Find out the value of maximum 30-minute rainfall for the given rainstorm; and calculate the intensity (I₃₀ in mm/h) for this period. And then multiply this value with the total KE of the storm. This is the value of EI₃₀. As note, for use of this value in USLE or RUSLE it must be modified in the unit of MJ mm (ha.h)^–1 and divided by 100, to get the value of factor-R.

Soil Erodibility Factor:

This factor is related to the various soil properties, by virtue of which a particular 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. In general, the soil properties such as the soil permeability, infiltration rate, soil texture, size & stability of soil structure, organic content and soil depth, affect the soil loss in large extent.

The soil erodibility factor (K) is expressed as tonnes of soil loss per hectare per unit rainfall erosivity index from a field of 9 percent slope and 22 meters as field length. The erodibility factor (K) is determined by considering the soil loss from continuous cultivated fallow land without the influence of crop cover or management.

The value of soil erodibility factor (K) can also be determined for a particular location, using a set of run-off plots of above specification (i.e., 9% slope and 22 m length) and measuring the soil loss for a long time and using the following formula –

Where,

K = soil erodibility factor

A₀ = observed soil loss

S = slope factor

ΣEI = total rainfall erosivity index.

The nomographic solution has also been developed for determining the factor-K. The procedure to determine the value of K, described by Wischmeir is shown in Fig. 21.1.

The values of erodibility factor K for use in USLE for different soils of India have been determined based on the runoff plot studies, reported by Singh et al (1981) are cited in Table 21.1.

The erodibility is a complex property of soil. As a common view, it refers to the ease by which a soil gets detach by raindrop splash during rainstorm, and/or by the shear force of overland flow or surface runoff from the soil surface. Physically, the soil erodibility can be viewed as the change in soil matrix after occurrence of rainfall. In other words, it can be expressed as the change in the energy state of soil matrix per unit applied external force or energy.

Conceptually, the soil erodibility reflects the view of getting removal of soil particles at different rates depending on several physical characteristics, such as texture, organic matter, structure and bulk density of the soil. As for as its definition is concerned, it is the rate of soil loss per rainfall erosion index unit, as measured on a standard unit plot. Practically, the factor-K is the average, long-term and soil profile response to the erosive power of rainstorm to produce soil erosion.

In real sense, it represents the detachment and trans­portation of soil mass by raindrop impact and flow of rainwater over the soil surface (overland flow/surface runoff). Numerically, its value varies from 0 to 1.0. The value of K = 0 indicates the soil to be very hard, which cannot get erode due to rainstorm. Normally, the rocks, stones etc., fall under this category. On the other hand, the value of K =1 reveals the soil to be very-very susceptible to get erode due to rainstorm.

Very coarse textured soils fall under this category. In this way, its value also represents relative toughness of soil mass to get erode on rainstorm occurrence. In brief, higher the value of K, greater will be the soil erosion. On the basis of several years’ investigations, a model relating more than 20 soil properties to soil erosion from standard erosion plots has been developed for K by Weishmeir (1962); the model is given as under –

Where,

M = organic matter content (%).

Si = silt content (%), 2 to 50 μm.

vfS = very fine sand content (%), 50 μ to 100 μm.

C = clay content (%), less than 2 μm.

S = total sand content (%), 50 μm to 2 mm.

A = structure (classes 1-4). The structural classification is shown in Table 21.2.

P = permeability class (within top 0.60 m). It is presented in Table 21.3.

For example, if Si is 20%; vfS is 10%; C is 10%; M is 2%; A is 2 and P is 3, then soil erodibility factor (K) would be 0.0197(metric). Note that above equation is used for the soils with the sum of Si and vfS fractions less than 70%. The textural parameter accounts for 85% of the variance.

Slope Length and Steepness Factor (LS):

The LS factor represents the erosive potential of a particular soil with a specified slope length and slope steepness. This factor basically affects the transportation of the detached particles due to surface flow of rainwater, either that is the overland flow or surface runoff. And accordingly affects the value of soil erosion due to any given rainfall.

The capability of runoff/overland flow to detach and transport the soil materials gets increase rapidly with increase in flow velocity. On steep ground surface the runoff gets increase because of increase in runoff rate.

The factors-L and -S are described as under:

i. Slope Length Factor (L):

The slope length is the horizontal distance from the point of origin of overland flow to the point where either the slope gradient gets decrease enough to start deposition or the overland flow gets concentrate in a defined channel. In principle, the longer the slope length the more runoff will be there; gathering the speed and gaining its own energy and thus resulting into rill erosion and formation of gully network. Zingg (1940) reported that the erosion gets increase exponentially (exponent = 0.6) with the slope length.

Wischmeier, Smith and Uhland (1958) reported that the ratio between erosion and slope length varies from year to year than from one site to another. They also found that the value of exponent varies from 0.1 to 0.9, is significantly affected by the change in soil, plant cover, use of crop residues etc. However, the effect of slope length on runoff is sometimes positive; sometimes negative, and sometimes nil, also, depending on the previous soil moisture content and soil surface condition.

Meyer, et.al. (1975) studied the effect of slope length on three sites with varying susceptibility to rill erosion. They showed that the effect of slope length was observed after a certain distance towards d/s and rate of increase in erosion varied depending on the soil susceptibility to rill erosion. This study indicates a kind of interaction between the effect of slope length and soil sensitivity to rill erosion, as presented in Fig. 21.2.

The unit plot’s data is used to derive the slope length factor (L), which is presented by the following relationship –

L = (b/22.1)^m …(21.8)

in which, b is the horizontal projection (m) of soil profile, as shown in Fig. 21.3; and m is the slope length exponent.

The value of m is related to the ratio of rill erosion due to concentrated flow to the inter-rill erosion caused by raindrop impact. It is expressed by the Fig. 21.3. Right angle triangle showing slope properties following relationship –

If the field slope is freshly prepared by using sub-soils, then the value of β may be doubled, because there is settlement of soil mass after few times; and accordingly the slope value gets affected. The value of β is taken as half for the soils under rangeland. If the soil erosion is due to runoff alone, e.g. by snowmelt then the value of m is considered to be 0.5.

ii. Slope Steepness Factor (S):

Steepness of land slope influences the soil erosion in several ways. In general, as the steepness of slope increases the soil erosion also increases, because the velocity of runoff gets increase with increase in field slope, which allows more soil to detach and transport them along with surface flow.

Surface detention of water is also reduced as slope increases. The depth of water collected on a level field dissipates the kinetic energy of falling rain drops and ultimately reduces the soil detachment, but it is not so on steep slopes.

The soil surface slope creates a significant effect on soil erosion by affecting the transportability of eroded soil mass from the land surface, along with scouring of soil from the moving path of runoff or overland flow. There is enhancement in runoff and soil erosion due to increase in slope steepness. The slope causes develop­ment of rills at hillsides. The slope intervenes the erosion by its form, gradient, length and position.

The forms of land slopes are described as under:

Forms of Land Slopes:

The slopes are found in different shapes or forms such as concave, convex, regular or wrap. The evaluation of effect of slope’s shape on soil erosion is very delicate procedure. However, in normal way this is neglected.

The possibility of formation of concave shape slope is mainly when field is exposed to severe soil erosion from long time, continuously. This is because of the reason that the base of field remains unaffected by the runoff, while middle portion of the field gets erode quickly than the top.

Wischmeier (1974) pointed that on passing of sediment from a smooth average slope towards concave slope area, the sediment transport gets reduce due to localized sedimentation. On the other hand, it gets increase when it passes on convex slope because of the gradient effect of steep face. In brief, the concave slope causes trapping, siltation and colluvial deposition of sediments. And at hill face the transport of sediment towards d/s is more.

Slope Gradient:

The slope steepness or gradient does not affect the kinetic energy of falling rainfall, but the KE of rainfall remains constant. On the other hand, the transport of eroded soil mass gets accelerate towards the foothill, because of increase in the kinetic energy of runoff.

The study reveals that when slope exceeds 15%, the kinetic energy of rainfall gets outweighed. Zingg (1940) reported that the soil loss increases exponentially with the slope gradient. The value of exponent for United States has been determined as 1.4. The relationship is given as below –

E = KS^1.4 … (21.11)

Roose (1967) found that the soil erosion and runoff both increase rapidly with minor variation in slope steepness (0.5%). He obtained the value of exponent higher than 2 for extensive crops providing ground cover, such as groundnut, maize and cassava. While Lal (1976) in Nigeria found that the soil erosion gets increase with increase in level of land slope, in the form of exponential relationship with m as 1.2 for the soil enrich with gravel in bare condition, but the soil loss is independent of slope (from 1 to 15%) when crop residues are left on the soil surface. Roose (1980a) also compared the rate of soil erosion of bare soils from the soils covered with pineapple plantations, burnt residues ploughed in, or left on the soil surface.

He found more than the proportional increase in soil erosion with increase in soil slope. And when residues were ploughed in, the erosion was very less on the slopes less than 7%, but at the slope more than 20% it was more than the tolerance level. When residues were used as mulch, then the rate of soil erosion was about to negligible even beyond 20% slope. These findings indicate that there is interaction between the effect of land slope, plant cover and crop residues.

The combination of slope length factor (L) and slope steepness factor (S) is called topographic factor (LS). Length and steepness of slope factors are combined together, is termed by a specific name topographic factor, which is defined as the ratio of soil loss from a field having specific steepness and length of slope (i.e. 9 percent slope and length 22 m) to the soil loss from a continuous fallow land. The value of topographic factor (LS) can be calculated by using the following formula, given by Smith and Wishchmeir (1962) –

Where,

L = slope length, ft

S = percent land slope

The slope length is measured from the point of origin of overland flow to that point where the slope either decreases to that extent at which deposition of soil particles begins or where the runoff enters the channel. Wischmeir and Smith (1978) again developed following equation for LS factor in M.K.S. system, based on the soil loss data obtained from the crop land on slopes ranging from 3 to 18% and length 10 to 100 m. The equation is –

In which, λ is the slope length (m), θ is the slope angle and m is a variable, depends on the steepness of land slope.

Mc Cool et al (1987) modified the slope steepness factor for use in Universal Soil Loss Equation, which is described, under.

Revised Slope Steepness Factor:

The slope steepness factor (S) of Universal Soil Loss Equation developed by Wischmeir and Smith (1978) expresses the effect of slope gradient on sheet and rill erosion. The form of equation was as below –

S = 65.41 sin² θ + 4.58 sin θ + 0.065 … (21.13)

In which, θ is the angle of slope. The factor S was evaluated for a given steepness, which is the ratio of soil loss from a particular slope to that from a 9% slope, when all other conditions remain same. The 9% slope is the steepness of the USLE unit plot. However, the condition of 9% slope does not satisfy in field conditions. Keeping this in view, Mc Cool et al (1987) have developed a set of slope steepness equation as a revised equation for S to use in USLE for estimating the annual soil loss.

These equations are outlined as under:

1. For Shorter Slopes not Greater than 4 m:

For this specific condition the S can be predicted by the following equation –

S = 3.0 (sin θ)^0.8 + 0.56 …(21.14)

In which, θ is the slope angle. The value of computed S is in percent.

2. For Longer Slopes:

For this condition the relationships were derived for the slope steepness less than 9% and equal to or greater than 9%. These relationships predict the soil loss more accurate as compared to the original USLE slope steepness equation.

The revised equations are as follows:

(a) Slope less than 9% –

S = 10.8 sin θ + 0.03 … (21.15)

(b) Slope equal to or greater than 9% –

S = 16.8 sin θ – 0.50 … (21.16)

These equations apply best to relatively smooth surfaces, where tillage is up and down hill, and runoff does not vary with the slope steepness above 8%.

3. For the condition, when erosion is mainly caused by the surface flow over thawing soil, the derived equations for S are given as under.

(i) Slope less than 9%

S = 10.8 sin θ + 0.03 … (21.17)

(ii) Slope equal to greater than 9%

(The 0.0896 represents the value of sin of angle of 9% slope)

The graphical presentation of topographical factor (LS) is shown in Fig. 21.4.

Crop Management Practices Factor (C):

The crop management factor (C) may be defined as the ratio of soil loss from a land under specific crop to the soil loss from a continuous fallow land, provided that the soil type, slope and rainfall conditions are identical. The crop and cropping practices affect the soil erosion in several ways by their various features, such as the kind of crop, quality of cover, root growth, water use by growing plants etc.

Since, these features differ significantly within the period from planting to the crop harvesting, therefore, the soil loss also gets affected. Similarly, the variation in rainfall distribution within the year also affects the crop management factor, which affects the soil loss accordingly. In general, the erosion effectiveness of crop and cropping practice is evaluated on the basis of five recommended crop stages introduced by Wischmeir (1960).

These five stages are given as under:

Period F: (Rough fallow) – This includes the summer ploughing or seed bed preparation.

Period 1: (Seed bed) – It refers to the period from seeding to 1 month, thereafter.

Period 2: (Establishment) – This is the time from 1 to 2 months after seeding.

Period 3: (Growing period) – It is from the period 2 to the period of crop harvesting; and

Period 4: (Residue or stubble) – This is the period from crop harvesting to the summer ploughing or new seed bed preparation.

For determining the crop management practices factor the soil loss data for above five stages is generated from the runoff plot, and C is determined as the ratio of soil loss from cropped plot to the soil loss from a continuous fallow land for each of the above five crop stages separately, for a particular crop, considering various combinations of crop sequence and their productivity levels. The weighted C is computed, ultimately based on the determined C values, stage wise.

Rao (1981), Pratap Narain et al (1980) and Nema et al (1978) have determined the values of crop management factors (C) for the common crops grown in the regions of Kharagpur, Koto and Vasad, respectively, given in Table 21.4.

The crop management practices factor (C) of USLE reflects the reduction in soil loss on growing of crops and application of proper management practices in view of development of good ground cover, as compared to the land without any vegetative cover.

The reduction in soil erosion/loss due to vegetative cover depends on the types of crop grown, cropping system, tillage practices and residue management practices followed. The crop management practices affect the erosion for the duration up to which they are capable to keep the surface rough or covered with crop residues or vegetations.

Numerically, the value of C varies from 0.003 to 1.0, in which the maximum value 1.0 is for the case of continuous fallow land; and minimum 0.003 is for excellent grass cover condition. The factor-C is thus the function of crop growth stages and the amount of residues lying on the soil surface.

The values of factor C of grain crops for different growth stages and residues and/or different tillage operations are presented in Table 21.5. The C value for a field in fallow, for different numbers of tillage operations is shown in Table 21.6. and the value of factor-C for the case when soil is covered by different materials is shown in Table 21.7.

The effect of straw residue and cropping sequence on C-factor has been presented by the graph, shown in Fig. 21.5.

Soil Conservation Practices Factor (P):

It may he defined as the ratio of soil loss under a given conservation practice to the soil loss from up and down the slope. The conservation practice consists of mainly the contouring, terracing and strip cropping, in which contouring appears to be most effective practice on medium slopes ranging from 2 to 7 percent. The soil loss from contouring ranges about one half of the total soil loss occurring from up and down hill farming system.

In general, as the land slope decreases from medium to zero, the effectiveness of contour tillage to reduce the soil loss gets decrease, as compared to the non-contoured tillage field. Similarly, when land slope increases from medium to steep slope, then contour row diminishes its capacity to reduce the soil erosion or loss, because of having a very little capacity to detain the water on soil surface.

In strip cropping, the meadow strips alternate with grain strips tend to slow down the surface flow, and thereby there is catching of eroded soil from cultivated strips.

Similarly, the terraces in hilly areas intercept the surface flow down the slope before attaining erosive velocity to damage the land. From field investigations, it has been found that when strip cropping is practiced with the terracing system, then it becomes more effective to control erosion and soil loss. The values of conservation practices factor (P) for contouring, contour strip cropping and terracing are given in Table 21.8.

The values of factor-P for different conservation practices are shown in Tables 21.9, 21.10 and 21.11.