in which ¡ is the slope angle. The values of f obtained from Eq. (4.20) have to be multiplied by 0.5 if the ratio of rill to interrill erosion is low or by 2 if this ratio is high.
Soil loss is much more sensitive to changes in slope steepness than to changes in slope length. In USLE, the S factor is evaluated by the following relationship:
in which 5 is slope steepness expressed as a percentage. The RUSLE has a more nearly linear slope steepness relationship than the USLE :
On steep slopes, computed soil loss is reduced almost by half with RUSLE .
The cropping management factor represents the ratio of soil loss from a specific cropping or cover condition to the soil loss from a tilled, continuous-fallow condition for the same soil and slope and for the same rainfall. The procedure for calculating the C factor requires a knowledge of crop rotation, crop-stage periods, soil loss ratio (SLR) for each crop period, and temporal distribution of rainfall erosivity. SLR values for the most crop rotations in the United States have been given by Wischmeier and Smith . To compute C, SLRs are weighted according to the distribution of erosivity during a year. The main limitations of this approach are the unavailability of SLRs for all crop covers (e.g., fruit trees) or vegetable crop rotations and the difficulties of transfering the SLR values calculated for American conditions to other regions.
To estimate the C factor for forest conditions, the procedure proposed by Dissmeyer and Foster  can be used. This is based on an evaluation of nine subfactors: amount of bare soil, canopy, soil reconsolidation, high organic content, fine roots, residual binding effect, onsite storage, steps, and contour tillage.
In the RUSLE, SLR values are computed using five subfactors expressing the prior land use, the canopy, the surface cover, the surface roughness, and the soil moisture status. The subfactor approach permits application of SLRs where values are not available from previously published experimental analyses .
The P factor mainly represents how surface conditions affect flow paths and flow hydraulics. The erosion control practices usually included in this factor are contouring, contour strip-cropping, and terracing . In the RUSLE, an update of the evaluation procedure for the P factor has been proposed .
Soil loss tolerance T is defined as the maximum rate of soil erosion that permits a high level of productivity to be sustained. The soil loss tolerance for a specific soil is useful for establishing soil conservation planning. The most common T value is equal to
10 t ■ ha 1 ■ year 1. If the USLE or the RUSLE is used for estimating soil loss, it results in
Equation (4.23) shows that slope length, land use, and erosion control practices are the three factors that can be practically modified for obtaining a given T value.
The prediction of sediment yield (i.e., the quantity of transferred sediments) in a given time interval, from eroding sources through the channel network to a watershed outlet, can be carried out using either an erosion model (USLE, RUSLE) with a mathematical operator expressing the sediment transport efficiency of the hill slopes and the channel network or a sediment yield model (MUSLE, WEPP) [93-95].
A physically based model is theoretically preferable, but its parameters, which are often numerous, may not be easy to measure or estimate. In addition, the measurement scale may not be at the same level as the scale of the watershed discretization for applying the model. Moreover, watershed soil erosion estimates obtained from physically based models are affected by the uncertainties in the equations used to simulate the detachment, transport, and deposition processes in morphologically complex areas. For this reason, a parametric approach, such as USLE and RUSLE, is a more attractive method even if the parameters have little or no physical meaning because they lump together both the effects of several different processes and inaccuracy .
Two different strategies can be followed for applying a soil erosion model at the watershed scale: (1) modifying the calculating procedure of the model factors in order to transform a watershed into an equivalent plot [94, 97]; or (2) dividing the watershed into morphological areas, that is, into areas for which all elementary factors of the selected erosion model can be evaluated [98, 99].
The first procedure allows the evaluation of total watershed soil loss, which then has to be coupled with an estimate of the sediment delivery ratio (SDRw) for the whole watershed to predict total sediment yield. The second procedure allows the calculation of soil loss in each morphological area, which has to be coupled with a disaggregated criterion for estimating sediment delivery processes to obtain sediment yield spatial distribution.
SDRw (% or dimensionless) generally decreases with increasing watershed size, indexed by area or stream length; the American Society of Civil Engineers (ASCE)  has suggested the use of the following power function (Fig. 4.27) :
in which k and n are numerical constants and Sw (km2) is the watershed area.
Spatial disaggregation of sediment delivery processes requires that the watershed be discretized into morphological units that have an irregular shape if they are bounded in such way as to define areas with a constant steepness and a clearly defined length
001 01 1 10 100 1000
001 01 1 10 100 1000
Figure 4.27. Comparison of different relationships between SDRw and watershed area Sw. Source: .
(Fig. 4.28). Discretization can be simplified by superimposing a regular grid with square or triangular cells onto the watershed area.
For each morphological unit, the sediment delivery ratio SDRi (dimensionless) has to be evaluated according to the following equation [102, 103]:
in which p is a coefficient that is constant for a given watershed, lpj (m) is the length of the hydraulic path from the morphological unit to the nearest stream reach, and spj (m/m)
is the slope of the hydraulic path. For evaluating y coefficient, the sediment balance equation for the watershed outlet, which states that the watershed sediment yield Ys (t) is the sum of the sediment produced by all morphological units in which the watershed is divided, can be used:
where Ai is the soil loss (t/ha) from a morphological unit that has to be estimated by a selected erosion model, Suj is the area (ha) of the morphological unit, and Nu is the number of units into which the watershed is divided. To apply Eq. (4.26), a soil erosion model at the plot scale has to be selected and measurements of Ys are necessary.
Using soil-loss data from plots or sediment yield estimates from a selected model, a potential relationship between radionuclide loss Y and sediment yield can be established [104, 105]. Thus, the spatial distribution of the sediment yield also can be deduced by the measured spatial distribution of 137Cs residual percentages Y.
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