The effect of topography on soil erosion results from length, steepness, uniformity, and the concavity or convexity of the area under consideration. On uniform slopes, total erosion on the slope has been found to vary with the slope length raised to a power that has ranged from 1.2 on slopes of less than 1% gradient (to the 0.2 power for soil loss per unit area) to 1.5 for slopes of 5% or greater gradient (to the 0.5 power for soil loss per unit area). There is some evidence that the value of the power may be larger for steeper slopes.
A wide range of relationships for the effect of slope steepness on erosion has been found in different studies. Plot data are usually collected from a narrow range of slope conditions to meet local or regional needs, and when extrapolated to either steeper or flatter slopes, or other regions with different climate and erosivity conditions, may give unrealistic answers. Simple empirical relationships for the relationship of soil loss to slope steepness have frequently been quadratic in terms of percent slope or a function of sine of the slope angle. The simplest form is the sine of the slope angle raised to a power b. The value of b has ranged from 0.6 to 1.4 in various studies.
Few slopes are uniform, and erosion rates are affected by the three-dimensional aspect of topography. Lateral concavity leads to more rapid collection of water into larger channels while still on the hillslope, and a higher average erosion rate. On a laterally convex slope, water disperses as it flows downslope, and erosion rates will generally be less than for a uniform slope case. As compared to a uniform slope of the same average steepness, vertically concave slopes have higher rates of erosion in the upper portions of the slope, and lower rates in the lower portions of the slope. If the lower slopes are sufficiently gentle, deposition may occur. Vertically convex slopes have lower rates in the upper portions of the slope, but greater rates in the lower segments. Compound slopes may have areas of deposition alternating with areas of detachment, creating a difficult situation to model. Convex areas of the same mean slope as a uniform slope will deliver more sediment off site than the uniform slope. Concave areas of the same mean slope will deliver less sediment off site.
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