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The Universal Soil Loss Equation was developed to predict the annual soil loss from field-size small areas. This equation does not compute the sediment yield from the watershed, directly.

To compute the sediment yield by use of USLE, the computed soil loss using USLE is multiplied with the delivery ratio of watershed. Since, USLE predicts the annual soil loss, therefore, only annual sediment yield can be determined by this equation, which is less important for design of water storage structures.

To overcome this demerit of USLE regarding prediction of sediment yield, Williams in the year 1975 made an effort to modify the USLE suitable for computation of sediment yield, either monthly or seasonal values. He modified the USLE by replacing the rainfall energy factor (R) with the another factor called ‘runoff factor’. For making this modification, he used the data of 18 small watersheds of Riesel, Texes Hastings and Nebraska.

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The form of Modified Universal Soil Loss Equation is given as –

Where,

Y = sediment yield for an individual storm (tonnes)

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Q = volume of runoff (acre-feet)

q_{p} = peak flow rate (cfs)

K, L, S, C and P are the factors of Universal Soil Loss Equation

This equation can also be applied to the large watersheds, if sediment sources are uniformly distributed in the watershed, and also if the watershed tributaries are hydraulically, identical. However, these conditions are not found satisfied in most of the large watersheds, which lead to cause the limitations for use of this equation to predict the sediment yield.

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However, this limitation can be eliminated by using routing functions. The sediment routing, using the modified universal soil loss equation is based on the assumption that, the sediment deposition is dependent on settling velocity of sediments, travel time, particle size and amount of sediments in suspension. This assumption is expressed as under –

in which, y is the sediment yield at an individual channel section; t is denoted as time; B is the decay constant, also called as routing coefficient and D is the diameter of sediment particles.

After integrating and simplifying the equation 21.39, it is obtained as,

Where, Y_{o} = sediment yield at upstream section.

T = travel time between two sections.

The sediment yield at a particular channel section can be calculated by substituting the values of Y_{o}, B, T and D in equation 21.40. To determine the total sediment delivered to the outlet of watershed (RY), the contributions of sediment from the sub-watersheds are added together, i.e.

Where,

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Y_{i} = contribution of sediment load from sub-watershed i, (tones)

T_{i} = travel time from sub-watershed i to the outlet of watershed, (hours)

D_{50i }= median diameter of sediment of sub-watershed i, (mm)

n and B are the number of sub-watersheds and routing coefficient, respectively. In above equation, the value of Y_{i} is determined by using the equation 21.39. The sub-watersheds should be so delineated, that the factors K, LS, C, P are uniformly distributed in each sub-watershed. The factor T_{i} is determined by flood routing method. The D_{50i} is obtained from soil information.

The determination of routing coefficient (B) is little bit difficult; to determine its value for an individual storm, for a particular watershed the factors K, LS, C, P and D_{50} are assumed to be constant, which revealed that the value of ‘Y’ obtained from equation 21.40 is equal to the value ‘RY’ computed from equation 21.41. Thus, equating the equations 21.40 and 21.41, i.e.

In which, D_{50m} is indicated as the minimum value of D_{50}. The D_{50m} is used as a constant value for determining the coefficient B. By this assumption the routing coefficient (B) becomes as the function of watershed hydraulics only, which reveals that if two watersheds are hydraulically identical, then they have equal ‘B’ value. The value of B is determined by iterative method, using the equation 21.43.

The above equation is applied to predict the sediment yield, when source of sediment in watershed is the sheet erosion only, but when floodplain channel scour and gully erosion are also there as sediment source to yield the sediment load from the watershed, then the equation will be somewhat different than the above.

In this case, their contribution for sediment yield must be fully included. The gully erosion is estimated on annual basis. However, for an individual storm the gully erosion can also be computed by multiplying the annual amount of sediment yield with the ratio of storm runoff to average annual runoff, i.e. –

Annual sediment yield x Individual storm runoff/Average total runoff

Williams (1975) mentioned that the sediment yield caused by gully erosion can be added to the sediment yield due to sheet erosion from the sub watershed and routed to d/s section, provided that D_{50} of both the sources is same but when it differs then both should be routed, separately.

In case of floodplain scour which is in the large watersheds, the sediment yield should be determined for each flow reach and routed to downstream. The sediment yield from floodplain scour in a given routing reach can be computed by using the equation 21.43 in following form –

Where,

YFP = sediment yield from floodplain scour at the routing reach (tons)

A = area flooded (acres)

R = runoff from watershed above the reach (inches)

In this equation the value of P is usually taken as 1.0, because there is no erosion control practice in the floodplain area. The value of factor LS is taken quite less, as slopes are normally flat. The factor ‘C’ is concerned, it is to be a dominant factor for floodplain scour, e.g. a floodplain covered by good crop cover, involves very less soil scour, but there would be severe scour on poorly covered flood plain.

The sediment yield resulted by channel scour can also be determined by using the equation 21.43. In this case, the factor ‘A’ (flooded area) is assessed by multiplying the channel length to its width. The peak flow rate is that which is resulted during a particular storm, passing through the concern stream. A greater value of LS is usually taken for the channels, because of greater slope due to side slopes and channel bed slope.

The factor C is also taken as a high value, because most of the natural channels are not covered by the vegetations. Similarly, the factor P is used as 1.0 because of absence of erosion control measures. In channel scour, the factor ‘K’ (erodibility factor) plays an important role to cause the soil scour from the channel section. For a channel which comprises a stable section, very small value of K is used.

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