Erosion modeling is the most widely applied method for producing a soil erosion map and for estimating future soil loss using present information. The main problems of using a mathematical model, especially if it is empirically based, are the knowledge of the input data and the need for calibration in the area studied.

For estimating soil erosion, physically based and empirical models are available. Physically based models simulate different hydrological (infiltration and runoff) and erosive (soil detachment, transport, and deposition) components of the erosive process even if empirically derived relationships are often used. Although the physically based models represent the future of soil erosion prediction, at present they are useful only for research purposes or in highly controlled experimental areas.

The most widely applied soil erosion model, which represents the best compromise between applicability in terms of input data and reliability of soil loss estimate [80], is the empirically derived USLE by Wischmeier and Smith [57], which has been revised recently [81]. Note that most of the available soil erosion models put some elementary factors of the USLE into their basic equations to estimate the soil loss or to simulate the subprocesses contributing to soil erosion.

The USLE was developed to predict average annual soil loss A (t ■ ha-1 ■ year-1) and is based on more than 10,000 plot years of runoff/erosion measurements:

R is the rainfall factor (MJ ■ mm ■ ha-1 ■ h-1 ■ year-1), K is the soil erodibility factor (t ■ ha ■ h ■ ha-1 ■ MJ-1 ■ mm-1), L is the slope length factor, S is the slope steepness factor, C is the cropping management factor, and P is the erosion control practice factor. L, S, C, and P factors are dimensionless. C and P generally range from 0 to 1 even if C can be as high as 1.5 for a finely tilled, ridged surface that produces much runoff and leaves the soil highly susceptible to rill erosion [81].

The storm erosion index of each event, Re, is calculated as n

in which I30 is the maximum 30-min rainfall intensity for the storm (mm/h), hj and Ij are the rainfall depth (mm) and intensity (mm/h) for the jth storm increment, and n is the number of storm increments. The R factor is calculated by adding the Re values of all erosive events occurring in a period of Nyears (N = 25-30 years) and dividing by N. For many regions of the world, isoerodent maps and simplified criteria for estimating R are available [82-85].

The K factor has to be estimated by the nomograph of Wischmeier et al. [86], which uses five parameters for estimating the inherent soil erodibility: percentage silt (0.0020.05 mm) plus very fine sand (0.05-0.10 mm), F; percentage sand (0.10-2 mm) G; organic matter content OM (%); a structural index SI; and a permeability index PI. The nomograph uses a particle size parameter M = F(F + G) that explains 85% of the variation in K. The full nomograph expression for the calculation of K (t ■ ha ■ h ■ ha-1 ■ MJ-1 ■ mm-1) is given by Rosewell and Edwards in [87] as

+ 4.28 x 10-3(SI - 2) + 3.29 x 10-3(PI - 3). (4.17)

In the revised equation (RUSLE) [88], a new estimate procedure for K factor takes into account seasonal variability of soil erodibility due to freezing and thawing, soil moisture variation, and soil consolidation. The proposed procedure is complex and needs the evaluation of the annual minimum and maximum value of the soil erodibility factor and the knowledge of the seasonal distribution of rainfall erosivity. The strongly empirical and geographical dependent nature of the procedure needs further verification for different zones. At present, it seems that the difference between the new and the old K evaluation can be more than 20% [89].

The slope length factor L is defined as

where X is the slope length (m) and the m exponent depends on the slope steepness s (m = 0.5 for s > 0.05). In RUSLE, the following expression for m is used:

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